7  I have fought the good fight, I have finished the race, I have kept the faith.
8  Now there is in store for me the crown of righteousness, which the Lord, the righteous Judge, will award to me on that day--and not only to me, but also to all who have longed for his appearing.

No link with the initial act of salvation, i.e., becoming a Christian.  It's only a statement that a path has been completed.  He has faith and he has done good works.  It does not say that you need works to qualify for salvation.  Also, "longed for his appearing" sounds like salvation comes from faith alone.  This is Paul at the end of an adventure, looking forward to heaven.

Mat 24:10-13

10  At that time many will turn away from the faith and will betray and hate each other,
11  and many false prophets will appear and deceive many people.
12  Because of the increase of wickedness, the love of most will grow cold,
13  but he who stands firm to the end will be saved.

This is encouragement to stand firm even when everyone around you is causing problems.  It says the struggle to keep on the right path is worth it in the end.  It does not say that the people who turned away lost their salvation.  Some of the false prophets may be people that teach that salvation is the result of good works instead of just faith alone.  Good works lead to a good life and God's favor.  It does not say that a person has to accumulate a sufficient number of good works to merit entrance into heaven.

Mat 7:21-24

21  "Not everyone who says to me, `Lord, Lord,' will enter the kingdom of heaven, but only he who does the will of my Father who is in heaven.
22  Many will say to me on that day, `Lord, Lord, did we not prophesy in your name, and in your name drive out demons and perform many miracles?'
23  Then I will tell them plainly, `I never knew you. Away from me, you evildoers!'
24  "Therefore everyone who hears these words of mine and puts them into practice is like a wise man who built his house on the rock.

What God asks, i.e. his will, is that we believe and do good things. The key phrase is, "I never knew you."  To know God is to have faith.  This section is saying that works alone is not what God wants.  God wants to know people.  He wants a relationship.  These people never had faith to begin with. They're just name droppers.  If we have faith, we are saved.  Then if we do good things, God is pleased.

Mat 25:39-46

39  When did we see you sick or in prison and go to visit you?'
40  "The King will reply, `I tell you the truth, whatever you did for one of the least of these brothers of mine, you did for me.'
41  "Then he will say to those on his left, `Depart from me, you who are cursed, into the eternal fire prepared for the devil and his angels.
42  For I was hungry and you gave me nothing to eat, I was thirsty and you gave me nothing to drink,
43  I was a stranger and you did not invite me in, I needed clothes and you did not clothe me, I was sick and in prison and you did not look after me.'
44  "They also will answer, `Lord, when did we see you hungry or thirsty or a stranger or needing clothes or sick or in prison, and did not help you?'
45  "He will reply, `I tell you the truth, whatever you did not do for one of the least of these, you did not do for me.'
46  "Then they will go away to eternal punishment, but the righteous to eternal life."

These people have neither faith nor works.  They're lost.

Rom 2:11-13

11  For God does not show favoritism.
12  All who sin apart from the law will also perish apart from the law, and all who sin under the law will be judged by the law.
13  For it is not those who hear the law who are righteous in God's sight, but it is those who obey the law who will be declared righteous.

This says to do good things don't just talk about doing them.  It does not say that works is a condition of salvation.  Righteous means that God likes what you're doing.  You're doing the right thing.

James 2:14-26

14  What good is it, my brothers, if a man claims to have faith but has no deeds? Can such faith save him?
15  Suppose a brother or sister is without clothes and daily food.
16  If one of you says to him, "Go, I wish you well; keep warm and well fed," but does nothing about his physical needs, what good is it?
17  In the same way, faith by itself, if it is not accompanied by action, is dead.
18  But someone will say, "You have faith; I have deeds." Show me your faith without deeds, and I will show you my faith by what I do.
19  You believe that there is one God. Good! Even the demons believe that--and shudder.
20  You foolish man, do you want evidence that faith without deeds is useless?
21  Was not our ancestor Abraham considered righteous for what he did when he offered his son Isaac on the altar?
22  You see that his faith and his actions were working together, and his faith was made complete by what he did.
23  And the scripture was fulfilled that says, "Abraham believed God, and it was credited to him as righteousness,"and he was called God's friend.
24  You see that a person is justified by what he does and not by faith alone.
25  In the same way, was not even Rahab the prostitute considered righteous for what she did when she gave lodging to the spies and sent them off in a different direction?
26  As the body without the spirit is dead, so faith without deeds is dead.

If you don't see any works there's probably not any faith there either.

(v. 2:18) "You have faith; I have deeds."  Show me your faith without deeds, and I will show you my faith by what I do.

He is saying, "I can show you that I have faith by what I do, you don't do anything so you cannot show me that you have faith."  This is encouragement to do good things.  It does not say that salvation is connected to works.

2 Pet 1:5-11

5  For this very reason, make every effort to add to your faith goodness; and to goodness, knowledge;
6  and to knowledge, self-control; and to self-control, perseverance; and to perseverance, godliness;
7  and to godliness, brotherly kindness; and to brotherly kindness, love.
8  For if you possess these qualities in increasing measure, they will keep you from being ineffective and unproductive in your knowledge of our Lord Jesus Christ.
9  But if anyone does not have them, he is nearsighted and blind, and has forgotten that he has been cleansed from his past sins.
10  Therefore, my brothers, be all the more eager to make your calling and election sure. For if you do these things, you will never fall,
11  and you will receive a rich welcome into the eternal kingdom of our Lord and Savior Jesus Christ.

It says to do good things and God will be pleased.  It does not say that you won't be saved if you don't do enough good things.  v.9 talks about a person who is saved but is missing the point about the need to do good things.  You're still your father's son even if he doesn't like what you're doing.  God will not abandon us.

John 10:27-30

27  My sheep listen to my voice; I know them, and they follow me.
28  I give them eternal life, and they shall never perish; no one can snatch them out of my hand.
29  My Father, who has given them to me, is greater than all; no one can snatch them out of my Father's hand.
30  I and the Father are one."

This is saying that to know Christ is to have faith and is to be saved (i.e. eternal life with Christ) and that a person will always be saved no matter who or what may influence them to the contrary.

Philipians 2:12-16

12  Therefore, my dear friends, as you have always obeyed--not only in my presence, but now much more in my absence--continue to work out your salvation with fear and trembling,
13  for it is God who works in you to will and to act according to his good purpose.
14  Do everything without complaining or arguing,
15  so that you may become blameless and pure, children of God without fault in a crooked and depraved generation, in which you shine like stars in the universe
16  as you hold out the word of life--in order that I may boast on the day of Christ that I did not run or labor for nothing.

To work your out salvation means to express your salvation in the works that you do.  It does not say continue to work to earn your salvation.

Philipians 3:8-17

8  What is more, I consider everything a loss compared to the surpassing greatness of knowing Christ Jesus my Lord, for whose sake I have lost all things. I consider them rubbish, that I may gain Christ
9  and be found in him, not having a righteousness of my own that comes from the law, but that which is through faith in Christ--the righteousness that comes from God and is by faith.
10  I want to know Christ and the power of his resurrection and the fellowship of sharing in his sufferings, becoming like him in his death,
11  and so, somehow, to attain to the resurrection from the dead.
12  Not that I have already obtained all this, or have already been made perfect, but I press on to take hold of that for which Christ Jesus took hold of me.
13  Brothers, I do not consider myself yet to have taken hold of it. But one thing I do: Forgetting what is behind and straining toward what is ahead,
14  I press on toward the goal to win the prize for which God has called me heavenward in Christ Jesus.
15  All of us who are mature should take such a view of things. And if on some point you think differently, that too God will make clear to you.
16  Only let us live up to what we have already attained.
17  Join with others in following my example, brothers, and take note of those who live according to the pattern we gave you.

Righteousness that comes from God is by faith, not by following the law.  Work to improve while looking to the future.  There's always something that can be made better.  Basic salvation is by faith alone, and just the beginning of the improvement process.

Eph 2:8-9

8  For it is by grace you have been saved, through faith--and this not from yourselves, it is the gift of God--
9  not by works, so that no one can boast.

This says that salvation is by faith alone.  Good works are good and God certainly wants us to do them, but you can't say that you have earned your salvation by doing a sufficient number of good things.