Hopefully you are signed up with a performing rights organization like BMI (see Is a Performing Rights Organization the Same Thing as a Publisher?. PROs collect money from radio stations (and other businesses that use music) and distribute them as royalties to songwriters. You can only get paid from radio play if you are affiliated with a PRO.
A cue sheet is a listing of the music used in a TV show or movie by title, composer, publisher, timing and type of usage (e.g., background, feature, theme) usually prepared by the producer of the program or film. Again, if your songs are registered, then the information will come automatically.
In a word, “No.” One performing rights organization (PRO) does not pay more than the others. If one paid more than the others, then all writers would be affiliated with that society. Over the life of a copyright, the payout on a song will be about the same from organization to organization.
No. This is a common misconception. PROs collect royalties for songwriters, composers and music publishers from radio, television, the Internet, restaurants and thousands of other businesses that use music. In effect, a PRO acts as a representative so writers can get on with the business of creating new music while their royalties are collected for them. There are three in the US: BMI, ASCAP and SESAC, and one in almost every country you can think of. (See “What does a publisher do?”)