i wouldnt place so much importance on the number of bars you see. if you look in settings/about phone how many db of signal do you have? do some speed tests and see what your upload/download speeds are. i use
this app but there are prolly others.
being rooted will let you run many different custom roms,and will likely boost your phones performance,including download speeds. if youre not happy being rooted its quite possible to unroot,no biggie.
as for the headphone volume,id think its possible,but i have no idea how youd go about doing it.
id suggest reading and researching the root procedure and and what folks are saying about the various roms theyre running. start with the stickys at the top,let us know if you have any questions