For problem #1. Did you try the things that people suggested to you in the other post. Just a question since you didn't mention what you have done to fix the problem
2) I see two problems here.
A) The sound quality with an FM transmitter will never be as good as
when you are hooking it to your stereo or amplifier with RCA
cables. Its just the nature of FM Transmitters.
B) Not only are you using unshielded RCA cables but you are using them
next to power lines in which case they will definatly pick up noise
Other than replacing the cables with shielded ones I don't know if
you can fix that.
3) May be related to problem 1. But I don't know. Try fixing problem 1 and
see if that helps
4) I have seen alot of comments that the lilliput screens are just plain low
quality. So you may not be able to do anything about that