1: I pretty much do that to. I start at the bottom, going down in short little spurts. Then I go back up a little further and finger detangle down. If I hit a bad know, I'll put conditioner and maybe a little extra water on it, then I pick it apart with my fingers.
2: Man, this question is hard because I pretty much have the same problem. Yes to Carrots is the best conditioner I've used in my hair for detangling and styling. I just really love it, even though it does cost slightly more than I want to pay for it. Sometimes Walgreens will have bogos on it, and so you could try shopping for sales. Tressume Naturals and GVP Conditioning Balm are suppose to be pretty detangling.
3: I feel like using a moisturizing leave in and having healthy hair helps prevent knots. Also, are you doing anything to protect it at night? Like, do you have a satin pillow case? Do you put it up when you go to bed? Maybe you could try a satin bonnet.