I think Paolini said telepathy over great a distances requires a lot of energy and a willing subject. That probably explains some of your questions. Paolini did write a long answer to some of your other questions over on his website: https://www.paolini.net/2016/03/16/telepathy-rules-limitations/

As for why Galbatorix didn't posses Murtagh when he was defeated. Well, he was assaulted by a spell that made him feel all the pain he ever caused so he wouldn't be in a condition to do that. On the other hand, Galbatorix could have possessed Murtagh at any time before his defeat or could have created a situation where Eragon and Saphira could then posses Murtagh to ensure they'd be captured. That always bugged me.