Minecraft – Can burning mobs set trees on fire

From the Minecraft Wiki:

"Lighting mobs on fire. This method deals damage slower and is less effective than using a sword, and one must click on a block below the mob rather than on the mob itself, rendering it a difficult way to kill."

So, to answer your question, I would suggest just sticking to the sword or bow.

Secondly, because sheep are mobs, you can light sheep on fire. They are no more flammable than any other animal or monster. (Except squid, of course)

According to the Minecraft Wiki, aggressive mobs won't wake you if you surround your bed with torches. Here is what it says about the mob behavior:

To ensure that you are not awakened unnecessarily during the night, the bed must not be placed along a 1 block thick wall, unless the area on the other side of the wall is also safe. If a hostile mob can get within 2 blocks of the bed, even if the blocks are separated by a wall, you will be awakened with the hostile mob standing next to you. There appears to be a slight delay before the mob attacks you, giving you time to get the first blow.

Edit: As of Minecraft 1.0, mobs will not awaken you suddenly if your bed is placed in an unideal location. Instead, the game won't let you sleep and will state that there are mobs nearby.