Its not really that complicated once you get into it. You only need to feed them like once every two or three days or so. Feeding them once puts 25 units of food in their pin which they munch on as time goes by (you can increase the ammount of food stored in their pin if you want to spend the money on it). I fed mine like two days ago and they still have 11 units of food to go through.
Also, the health and happiness can be increased at the same time using certain items that can be bought from the market (such as hydrating cream) so that takes some of the complexity out of careing for your critters. As far as the puzzle pieces go...all I can say is just hover over them and figure out what they do, and try to build your skills based on what effects you are going for/have available.
When you go to create a new creature, different parts (horns, tails, dorsal fins, etc.) Give different pieces to include in skills. Apparently its also possible to splice two creatures into one to get new skill pieces, though you need a special item for that.. I think you get it from questing. (go to downtown and figure out what sample you need to get, then go on safari in the designated area and try to get it.)