OK.
First of all do not worry about the hop residue, trub etc... It's not going to hurt your beer and it will settle out in the primary.
Second. A screen is useful. I use a bazooka screen on the inside of my kettle. Note: I also use leaf hops. For pellet hops, you might consider something
like this. (In the first post, the pictures have been deleted, but you can read through the thread to see them all.)
For siphoning, you should invest in an autosiphon. A regular siphon will work too. Just make sure the carboy is higher than the bottling bucket.
I think I hit all of your questions.
Good Luck.