Overall weight gain during pregnancy should be between 10-15kg. If your wife experienced bad morning sickness during her first trim, she could have lost some weight then and then now starting to put some weight back on, thus the seemingly slow weight gain. As long as she is eating nutriously and healthily, not skipping meals and filling her tummy when she is hungry, it should be ok. She can drink milk to boost the weight gain.
During my 20wks, I only feel the baby's kick here and there. Most times I'm not sure if it was the baby kicking or I was sitting in a bad position or what. The kicks became more obvious after my 25th week and my husband could literally see the baby kicking and feel the kicks too when he places his hand on my tummy.
Your wife should be going for a detailed scan soon during 20 weeks and you can see the baby's movements during that scan. You should be able to tell the gender too if your baby is not shy.