Hi Keat, playing with the beat only improves if you learn to count out loud , don't be shy just do it like a kid has to learn to count in school.This helps to concentrate on the beat more then on the singing ( with other words; it helps you in not getting distracted so much )

About branching out; don't put more on your plate then you can eat or learn to crawl before you can walk. You can not be a lead player without knowing chords and the theory behind it all.

Regards from an old player with lots of experience

Herman