Puppy toilet training not going so well..... help please.?

Hi, my pup is 10 weeks old have had her for only just a few days due to not being wanted at her previous place, how could i say no she is adorable anyway this is my 1st pup so very new to all this. Right, ive been keeping her in my kitchen at night time with paper to pee pee on and 4 blankets for her to snuggle to, she will happily pee and poo on the paper the whole night but as soon as she is out the kitchen she will just go where ever she is standing, she is half pom half chihuahua so very small so i hardly ever actually catch her in the act which is making things so hard, when i have found the accidents i don't tell her off as I don't want confuse her, anyone had the same problems. She also really cries when i go out the room, is this normal? she usually stops after 10-15mins of going bonkers to start again at 4.30 in the morning, Thanks in advance