I don't think you should delete the posts. Why is ok for parents to ask endless questions about teachers and other children and not ok for a teacher to ask advice about one of the class members
. Bit hypocritical 
It sounds like the child has low self esteem. I agree that the parents should stop with the extra work at home and go out and do fun things with him. Remind them to praise the effort, not the result. Also, let him know it's ok to fail and get things wrong.
Does he do lots of things for himself at home. Age appropriate responsibilities at home (washing up, making his own packed lunch, making his bed, setting the table, etc.) will all help raise his self esteem.
Practical issues - is he getting enough sleep and does he eat well and have friends to play with. Is he getting enough positive attention.
Are there any family changes, new job, sibling moving schools, grandparent unwell, any change of routine.
In school, carry on with the rewards. Consider a 'now and next' chart - first you do this, then you get to do that (reward).
Hope some of this is relevant.