A few problems with touch

so ive been having a lot of fun with my ipod touch with the customizing tools and such. however, ive recently encountered a few problems. first off, when i try to connect the ipod to a charger or to the computer through the usb cable that came with it, it does not always work correctly. sometimes it says that it's fully charged when it really is at about 20%, and sometimes it wont even recognize the connection.

the second problem i had is that ive added a few album covers to my music in itunes, but the covers arent syncing to the ipod.

the last problem is that whenever i install something onto the touch, it tells me that i am running out of disk space and that i should delete some music or video files. when this first happened, i checked how much space i had left and i found that there were around 4 gigs free.

if anyone can help me out with any of my 3 problems i would appreciate it a lot! thanks!