'Kay, I'll try to answer these to the best of my knowledge. Making it so that both genders are able to relate.
What would you do if the person you like hasn't been talking to you lately? Should you just move on or continue to persist?
Most people automatically assume, "Oh, he/she hasn't been talking to me lately, I must've done something wrong and he/she must hate me."
FIrst, consider this. Have they been acting differently towards anybody else? If so, maybe they're going through a tough phase in their life. Don't take it personally. Go and talk to them and try to coax out of them what's wrong. If you don't feel like they'd tell you or it would make things worse, give them some space. They will most likely come around eventually.
They could also, for instance, be busy. Everyone has some kind of a life and they may not have enough time to catch their breath. In this case, just give them some space and they'll probably start talking to you again.
If they've only been treating you differently, then think why. Have you done anything displeasing? Have you told any of your friends that you like him/her? Maybe your friend told the person you like that you like him/her and he/she is avoiding you. If that's so, still give them space, but spend a little time talking to your friends.
Don't fuss over it too much unless you know you've done something that they don't like. If that's the case, apologize.
What do you do if the person you like likes someone else? Should you move on or fight for him?
Man I hate this situation.
Personally? I wouldn't fight. I would say to myself, "Okay, it's a fact that he likes someone else. I'll live." I hate fighting over people. But I'm not the type who's going to give up hope either. I'll just stand there and keep watching, keep hoping. If you truly care for someone, their happiness is more important than yours. You like her? Alright, go for it. I'll stand here and cheer you on, because I care for you in a way that I'm willing to make a sacrifice on my own part if it'll make you smile.
You can't have a true and good relationship if you don't have a mutual feeling. And liking someone beyond friendship isn't something you can force out of anybody.
However, that's my take and opinion on the situation. Since this happens more commonly for those who are friends in the beginning, keep up your friendship and keep smiling.
What's the best way to keep troublesome kids calm? How can you keep them quiet or entertained long enough so you can rest?
You seem to be looking towards the "kid should be independent enough to do his own thing and leave me alone." That means, in most cases, two things.
1. TV
2. Computer
These are the two most commonly used methods by parents these days to keep their kids entertained. You can also look into their interests and have them do painting, coloring, reading, (if you have a backyard) playing outside with you watching them, etc. This tends to be for kids who are more independent though.
However, if the kid needs to do homework or something, this is how you do it.
"Ok. You finish your math homework and you can watch 15 minutes of so-and-so TV show." or "After you finish 2 pages of your homework, you can take a 10 minute break." Really, kids are externally motivated so you need something to get them working and doing the job.