Yep, soundsreally normal...

YOu cant overfeed a breastfed baby hon, so dont worry about offering the breast too much - especially at such a young, young age.

Like others have said....plenty of wet nappies.

Babies at such a young age are going to be sleepy anway....as well as in your breastmilk is a hormone that gets released, that makes baby sleep....and you sleepy. So its only natural that she may fall asleep at the breast. Maybe she's not actually hungry...rather wants to suck/and go to sleep....

Its all trial and error hon...your both learning this.....it will take a little time, but you both will get there...