I haven't gotten to this point but I'm assuming it's either like virtual families where you just get a new mayor, or you have to start over. I'd play it safe and just adopt a child.

If she is feeling lonely you can tell her to follow you around for a while. If you don't it's my going to hurt her or anything

This is true. You can hand deliver crops to your citizens. First what you have to do is grow a garden/food and when they are ready to harvest go over to them and select take. Once you have done that to each plant, the food should have been placed into your inventory. After that, look around to find a citizen and from you inventory take a potato, carrot, tomato, etc. and place it on the person. They should put their hand behind their back which means they have been fed. if you don't want to go through the trouble of doing that everyday then they will eat themselves. Just make sure you plant plenty of food so they don't starve

It does not say whether or not you should. From what I've seen it doesn't make the town more beautiful do it attracts other people to come live in your town so it's purely your preference. Even if you do cut down trees, you can always replant them by buying more seeds from the store.

If you mean normal trees (fern, maple, etc.) Then buy an axe from the store and with the axe in your hand double tap on the tree and your little person should hit the tree. Do this 3 times and the tree should fall over. For other trees you might have to use more advanced axes.