I think, it could be some health problem with her that's why his pad is hot. You should take her to the doctor for vet. It will be ok.

Definitely, they can sure. As we all know they can't say anything but they can express the bad or good mood.. So, it happens..

There is no problem to pick them up but for now let them be with their mother, she knows best how to get them used to theirenvironment. After that you can.

Yes, this is normal. Actually due to medicine and tiredness he feel sleepy. After few hours, he will be ok.

Kitten always love to play and cool places to enjoy. Bathtub is really the most enjoyable place for cat.