My LO is 20 weeks and I am still paranoid and always have tons of questions! hehe
1. My LO was 7lb 13oz at birth. By the time we were discharged she was 7lbs. At her 1st dr's appt at 5 days she was still 7lb. It was so hard for us to get her to put on weight. It turned out she was tongue tied and once her frenulum was cut she did start putting on weight. It definitely took us longer than the recommended 2 weeks for her to put all of her birth weight back on but it happened eventually. Every baby is different and as long as they are producing enough pee and poop diapers then it's okay. LO is now 14lb 2oz and in the 54% for weight. :)
2. Yes, I can hear LO swallowing when she's eating. As long as she isn't choking then that's fine. That's great that she's burping on her own throughout the day, too!
3. LO's poops vary from peanutbutter greenish to runnier seedy yellowy looking. Trust me, you'll know when it's diarrhea! It'll be just like brown water, literally! Also, if it seems like she is pooping more than she's eating then it could be diarrhea but if that's not the case then you're fine. LO's all have their individual poop schedule. I've seen some who poop everytime they eat and others like to go constantly in the bathtub (like mine! hheeh) or right after a bath.
Hope this makes you feel better :)