Well, take care of it. Feed it when it loses "hungry" hearts and play with it when it loses "happy" hearts. Treats are ok, but only give it treats if it won't play games and you're lazy. If you don't want to give it treats at all (which some would argue gets you better characters) you can wait until it eats again and then play games with it. Praise it when it cries or is turned around, and Time it out when it calls but has semi-full hearts. Clean up poop when it poops, and try to catch it when it's about to poop. When you see wavy lines on both sides of your tama and it looks a tad constipated, press the toilet button (3rd on the top row) and your Tama will use the toilet instead of going on the ground. (however, there are no apparent benefits that catching it before it poops is in any way different than catching it afterwards. It will not raise training bars. Some claim that it potty trains it so that the Tama will go on the toilet itself, but there is no proof to proove that) Also, turn out the lights when it falls asleep or yawns (turning out the lights when it yawns gains a "happy" heart).
2. Does your Tama fight?
No, they don't. They play games that involve blowing up balloons and eating. They can also give eachother gifts.
3. Give some tips on how to grow.
Wait. Follow the instructions from number one. There is no way to make your Tama grow faster than normal. It will grow when it's ready. However, you can slow down growth by pausing your Tama (hold down A+B simultaneously).