4 Answers

You can if the child or children spends the majority of time in your home. 

That would be determined in court.  If there is a large variance in the parents' income levels, some assistance might be requested; the judge would make the determination. Nobody should feel he/she is "entitled" to anything. 
The only one(s) entitled to anything in situations like this are the child(ren).  You figure out what I'm talking about. 

If one parent is proven to be unable to afford the upkeep of the children whilst in their care and the other is financially stable yes. For example a stay at home dad, living on a benefit/pension may be entitled to assistance with regards to child support whilst the children are in his care if his spouse is working

In a shared custody case, I don't think support is ordered unless they just want to go back and forth....