Hello Pantsy and welcome!

Is there a method that allows one to lucid dream without waking with the aid of an alarm clock?
Yes, DILD. It's when you are in a dream, and realize you are dreaming, causing you to become lucid. This can be done with RC's, some people also have noticed patterns in their dreams so they can realize it by seeing them.
Link to DILD guide.

Is there any easy way to fall asleep?
Hmmm...I'd have to say it differs from person to person. Some people can fall asleep instantly, others, like me, it might take longer.
There's not really an easy way, you can try completely relaxing, meditating, and clearing your mind. Listening to calming music maybe?

Is there a position for lucid dreaming that is both comfortable and effective?
Whatever position you normally sleep is the best. As far as I know, there is no correlation between sleeping position and lucid dreaming.