We don't have faith. It is God who grants us faith.

Lutero said:

No.

1. We don't have faith. It is God who grants us faith.

a. non-sequitur. If God has granted someone faith, then that person has faith.
b. We don't have faith. That is true. 
i. Faith is demonstrated by works. If you have no works, you have no faith.
ii. Those who love Christ, keep His Commandments. If you, as most Protestants, deny that keeping the Commandments is necessary, then, ipso facto, you have rejected Christ.

2. We're saved by Christ's atonement.

Those who love Christ and obey Him are saved by Christ. However, you claim to save yourself by your FAITH ALONE.

God elects.
God sent His Son.
God provided Himself as the propitiation for our sin.
God calls.
God regenerates.
God grants us faith.
God grants us repentence.
God Justifies.
God sanctifies.
God glorifies.

What does your God do?

That is why my God does. My God also justifies, those who keep His Commandments:
Romans 2:13
King James Version (KJV)
13 (For not the hearers of the law are just before God, but the doers of the law shall be justified.

Romanos 2:13
Reina-Valera 1960 (RVR1960)
13 porque no son los oidores de la ley los justos ante Dios, sino los hacedores de la ley serán justificados.

Really? You've kept God's commandments? Are you confident enough in that claim to put it to the test?

Are YOU going to put me to the test? And what would that test do? But again, since you seem oblivious to the fact that it is God who decides who is saved, you put yourself in His place as though you actually had the power to save and condemn. 

But here, let me put your faith to the test. Abraham had faith. And because he had faith, he left his household not knowing where he was going. He was over 100 years old and yet he came together with his wife, even though his body was near dead and they conceived a child.

How do you demonstrate your faith in your works? You deny the need to keep the Commandments. So what does that say about your love for Christ?

...through works.

Faith is demonstrated by works. And the washing of Regeneration and renewal of the Spirit, is a work of GOD.

God saves those He chooses to call, in spite of their inability to obey His Word.

It is clear from Scripture that God saves those who OBEY His Son:
Hebrews 5:9
And being made perfect, he became the author of eternal salvation unto all them thatobey him;

And you really believe that you're saved by your faith?

If I am to be saved, God will save me. Not you or me or anyone else. God.

But God only saves those who keep His Commandments. And since you deny His Commandments, but claim salvation by your faith ALONE, then you must be saving yourself.

The Catholics here tell us all the time that they were saved by being baptised.

Scripture tells you that:
1 Peter 3:21
The like figure whereunto even baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ:

But you won't believe Scripture.

And we don't mean OSAS either. Because Scripture says also:
Hebrews 6:4-6

King James Version (KJV)
⁴For it is impossible for those who were once enlightened, and have tasted of the heavenly gift, and were made partakers of the Holy Ghost,
⁵And have tasted the good word of God, and the powers of the world to come,
⁶If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame.

When I talk to Catholics on the street, I get a variety of answers: "I'm going to Heaven because I'm a good person". "Of course I'm going to Heaven. I'm Catholic!" "Well, I was baptised when I was little." "There's no way to know whether or not I'm going to Heaven."

I doubt it. The answer I've always heard from Catholics is the last one. "I don't know if I'm saved. God knows." It is one which is heavily criticized by Protestants who are accustomed to putting themselves in God's place and judging their own and other peoples eternal destiny. But Scripture is clear:
1 Corinthians 4:5
Therefore judge nothing before the time, until the Lord come, who both will bring to light the hidden things of darkness, and will make manifest the counsels of the hearts: and then shall every man have praise of God.

Every now and then, I'll get a vague answer about Jesus but then, when you dig a little deeper, you find that they don't really understand what Christ did, why He did it, or how He applies it to us.

The problem is that YOU don't understand what Christ did:
1 Peter 2:21
For even hereunto were ye called: because Christ also suffered for us, leaving us anexample, that ye should follow his steps:

You think that Christ died in order to give you a free ticket to heaven. You deny His Commandments:
John 14:15
If ye love me, keep my commandments

You deny that you must obey Him:
Hebrews 5:9
And being made perfect, he became the author of eternal salvation unto all them thatobey him;

You claim that you deserve salvation by your faith only:
James 2:24
Ye see then how that by works a man is justified, and not by faith only.

Then you claim that Catholics are confused but it is YOU.

Careful, lest you fall into the same ditch the Catholics are in. Leaving the RCC is a response to salvation, not a means of salvation.

The Catholic Church is the means to salvation which Christ instituted upon this earth. It is possible to be saved outside the Church. But it is very difficult:
1 Peter 4:17
For the time is come that judgment must begin at the house of God: and if it first begin at us, what shall the end be of them that obey not the gospel of God?

What greater evidence is there that they believe in works righteousness than Purgatory?

On the contrary:
1. We believe in FAITH and works. As Scripture says:
James 2:18
Yea, a man may say, Thou hast faith, and I have works: shew me thy faith without thy works, and I will shew thee my faith by my works.

2. Purgatory is described in Scripture:
1 Corinthians 3:10-15

King James Version (KJV)
¹⁰According to the grace of God which is given unto me, as a wise masterbuilder, I have laid the foundation, and another buildeth thereon. But let every man take heed how he buildeth thereupon.
¹¹For other foundation can no man lay than that is laid, which is Jesus Christ.
¹²Now if any man build upon this foundation gold, silver, precious stones, wood, hay, stubble;
¹³Every man's work shall be made manifest: for the day shall declare it, because it shall be revealed by fire; and the fire shall try every man's work of what sort it is.
¹⁴If any man's work abide which he hath built thereupon, he shall receive a reward.
¹⁵If any man's work shall be burned, he shall suffer loss: but he himself shall be saved; yet so as by fire.

3. Purgatory is a work of God. In Purgatory, God cleanses our sins.

But you reject Christ when you deny that you need to keep His Commandments. It is written:
John 14:
²⁴He that loveth me not keepeth not my sayings: and the word which ye hear is not mine, but the Father's which sent me.Therefore it is clear, those who do not love Christ deny His words. And Christ said that keeping the Commandments is necessary. Protestants deny Him.

Sincerely,

De Maria