1. Yes.
2. It depends....
As far as the plane itself, it should be ok as long as the rain isn't too heavy, and there's absolutely NO LIGHTNING<===IMPORTANT, read it again.
Make sure that any wood is very well sealed(fuelproofed). Make a good seal between wing and fuse, balsa soaks up water quick, and gets heavy. Water(yes, even rainwater) is BAD for electronics, including transmitter. If you insist on doing it, bag the electronics inside the plane(ziploc baggie or equivalent, rubber band tight around bag opening to allow wires to exit), same goes for the battery. In effect, you're waterproofing the plane. A plastic garbage bag over the transmitter, with a small hole for the antenna works well, but be sure to point the antenna slightly DOWN so water doesn't run into the Tx, instead just drops off the end. The engine should be fine as is, as long as it's not raining too hard. Keep in mind, it only takes one fairly good sized drop of water to kill the motor.... always be ready for a deadstick landing. (N/A for electric- no problems there, usually) Keep your fuel sealed up tight, it attracts moisture and ruins the fuel. When done flying - dry everything off thoroughly as soon as possible!
If it's been raining for a while, watch out for mud. As it builds up, it makes a plane progressively heavier&heavier to the point where it won't get off the ground. (don't ask how I know )

Other than that, have fun!

Edit for spellering...