Firstly, congrats on your new bubba!

Breastfeeding is a unique relationship, and takes some time to establish. Some experts say at least 3 weeks to get supply established, but for many of us it takes a lot longer. You are doing so well!

At this early stage I would be giving bub unrestricted access to the breast. I know a routine is your goal, but at this stage, establishing your supply is more important I would think. I would definitely not be advising water. Breastmilk is all your baby needs!

As for the fussing, it sounds like she is falling asleep before fully draining the breast...so she might be getting too much foremilk and not enough hindmilk, which will fill her up (and make her sleepy). Can you wake her when she drifts off? Or let her doze for a bit and then pop her back on. I would put her back on the same side to ensure she is draining the breast, before offering the other side (I have only ever fed from one breast per feed, so the whole swapping thing is new to me).

As for the routine, it really wont take long to establish, once you and your baby know each other a bit better. Try and enjoy these early days (daze!) and see if a natural routine falls into place. Breastfeeding and routines can be tricky, because your baby will fuss at certain periods to build up your supply for the next growthspurt. But I think you will feel more confident imposing a feeding schedule once you know bub is thriving.

HTH

ETA: For the moment, I would actually recommend not timing feeds or looking at the time between feeds...it will do your head in. My mantra was always, my baby has a relationship to my breast that doesn't involve me. I always fed her whenever she cried...breast is so much more than food! None of us know what we are doing in the early days, just remember you are doing brilliantly and before long you will have this all under your hat and be advising other new mummies!