Student or Learner
1. Does "do our children any favors " mean "we give them some benefit like becoming independent"? "favors" sound a little bit awkward other than its normal meaning.
2. Does "take over" mean "get a resposibility from someone"?
3-2)Do not do too much for your children. Children learn to do things independently by trial and error...When your children want to have frriends over to play, do you have them call their friends themselves? It is natural for us as parents to want to protect our children from things painful or difficult. But sometimes we do not do our children any favors when we take over for them. By doing so, we give children the message that they are not capable of doing anything for themselves...
not a teacher
"we do not do our children any favors" = we are not helping them in any way, or as you suggest, not allowing them any benefit from the situation.
To "not do (someone) any favors" is a common phrase with this meaning.
Here, "take over" means to insist on doing simple things that the children could do themselves, and hence learn by. For example, calling their friends to invite them over, rather than letting a child make the call.