Putting hands in mouth is an activity for them. If the baby is on bf then pee count should be 6+ , weight gain should be proper, baby should be active.

Putting hand in mouth doesn't mean baby is hungry... It may sign of teething. If baby is getting cranky, not gaining weight and looks tired every time that means he is not getting proper diet

Not gaining weight, less than 6 urine count can be sign of not getting enough milk. No putting hands inside the mouth doesn't mean baby is not getting milk. Baby is exploring, relax.