Yeah, it's normal and perfectly ok.
Remember that the babys' stomach is only about as big as a marble for the first few weeks or something like that. I'd have to look it up again to be sure, but I was amazed at how really tiny their bellies are. No wonder they spit up, they keep overfilling their tanks!
Breastfed babies don't burp the way that FF babies do, since they get fewer air bubbles. The still do occasionally burp, but you don't have to force the issue. With DS if he had enough air to need to burp, he's be cranky after a feeding until it came up, usually with a fair amount of breastmilk too. No worries, your supply will be plentiful enough to make up for what doesn't stay down. it will look like breastmilk when it comes back up, sometimes slightly curdled, and often very spitty. This is normal too. It won't look like characteristic vomit really.
Hiccups and lots of sneezing are normal. The baby still has a little fluid in the smaller pockets of the lungs, and the hiccups and sneezes help move that fluid out. Some babies, including my own, cough up fluid and swallow it, and then spit it up, fire-extinguisher style, all at once when the belly is full. Don't panic if your baby pukes clear fluid every now and then, this is just the amniotic fluid coming up. The more, the better, cause every little bit is less that's in her lungs.
No problem about the back laying, just keep the baby close, along with plenty of dry cloths for wiping. Turn the baby to the side to help the spit up drain away from the mouth, or even face down in your arm. Just wipe him/her off as best as you can, she'll be fine.
