John wrote, "And by this we know that we have known Him, if we keep His commands" (1 Jn 3:2) Is John saying that we should base out assurance of salvation on our works?

Here's what I think ... The issue at hand in 1 John 3:2 seems to me to be about a congregation and how people within the congregation prove to each other they are saved. Ask yourself. How can we know we are part of a congregation of believers and NOT a congregation of fakes, pretenders and false professors?

"And by this we know that we have known Him, if we keep His commands" (1 Jn 3:2)

A man knows he is part of a TRUE congregation -- an assembly of believers -- when he sees those around him OBEYING the commands of God. He can't see the hearts of the other believers. It's impossible for him to see into their mind, and see their faith directly. So the man can only know he is part of a true congregation if those around him are keeping God's commands.

Imagine an outsider came to a congregation and said "You are a bunch of fakes. You say you believe, but you don't practice what you preach. Hypocrites!"

The Apostle John would have responded, "No! We know we have known him, [because] we keep his commands."

Obedience to God is 1) the way believers prove to each other they are saved and 2) the way a congregation proves to outsiders that it is a true congregation, and not made up of hypocrites.

Jonathan, you also asked about 1 John 5:13

===  I wrote these things to you, the ones believing in the name of the Son of God, that you may know that you have everlasting life, and that you may believe in the name of the Son of God. ===

Now, obviously the people John was writing to already believed in Christ. So why does John say, "I wrote these things ... that you may believe in the name of the Son of God" ? Is John saying that they needed to be converted? Of course not. John wrote to REMIND his readers about Christ whom they already believed in. He wrote so that they would continue to believe in Christ. In the same way, John reminded them that they had everlasting life too.

Please read 1 Peter 1:12, where Peter says, "For this reason I will not neglect to cause you to REMEMBER always concerning these things, though you know and have been confirmed in the present truth."

Peter and John both wrote to cause their readers to REMEMBER the truths about Christ and how he saved them. In fact, Peter states that his readers already knew they had "been confirmed in the present truth". "You know and HAVE BEEN CONFIRMED".

Past tense!

John and Peter wrote to remind their readers of what they already knew.