Barre chords take a lot of practice to get your fingers used to them. I recommend just once for a few minutes every day going up and down the neck playing the basic F F# G G# A A#... barre chords. Eventually your fingers will build and stretch the muscles necessary to play barre chords.
Palm muting is used in more than just power chords. It is used in rhthm and just... a lot of things. How you do it is by placing your fingers over the string so that it mutes the strings.
Some fun songs for you to learn that would be fairly easy would be Wild Thing, Teen Spirit (Nirvana), Polly (Nirvana), and other stuff... Well I hoped I helped you a little bit. If not... atleast I tried. Also for more mellow songs I recommend learning to play song from Jewel's first album. It develops fingerpicking skills.