1/-Passing Stool upto 6-7 times a day can be normal in child of this age.
2/- Keeping hand in mouth or putting any object in mouth is also normal part of development as he is Having oral phase of Psychological development. He would like to explore his mouth till 15 - 18 month. Then he might start exploring his genital. That’s normal.
3/- Teething is normally round 8-13 months .
4/- You should keep burping your child till he grows little older , upto 12-15 months .
Next Steps
In case Stools are water or bloody, you should consult a pediatrician