I've been to (not inside) Paradise Falls and have introduced myself. (My character, named Tranquil, is a gentle person who wants to help everyone, except Raiders and Mutants!) I have also been to and inside Lamplight Caverns, talked with the Mayor but he doesn't ask me to save the kids penned up in Paradise Falls. How do I start that? I can get inside Paradise if I pay [censored] 500 caps but I don't want to do that.

Second question: is there some way to load all the tips the game offers every time I start it up? They go by so fast I can't quite read to the end in a lot of cases. The one really valuable one I picked up was to shoot Mirelurks in the face because that's where they're unarmoured and vulnerable. Up till then they drove me crazy.

I've never initiated the quest from the mayor, because when I hit Paradise Falls, I find a kid hidden behind some wrecked cars, outside the entrance, who asks me to save them.

Paying the 500 caps is your best option at this point, because every other option turns the town hostile, which won't fit your character profile too well, though it's moot because the town's going to go hostile on you the second you release those kids.

I say if you don't want to pay the caps, sneak in and shoot them all.

Question 2: I've not seen any way retrieve tips in the game, but http://fallout.wikia.com/wiki/Fallout_3_loading_screens, if you want to see them all.