Can My Wife Get Child Support If I Keep My Child 50% OF THE TIME?

Several factors play here. First if you have the child(ren) 50% of the time or more, (NOT LESS) and/or your wages are about equal? Then its a white wash because both parents are considered
equal in contribution to the child. As soon as the scale tilts more to the other half's favor than you could be expected to contribute support. Also the ex may try to sabotage your efforts for 50% if she is "money hungry". I have seen 50/50 parenting work when both couples make it work.

On the other hand when one member wants to sabotage the custody issues for "monetary gains"
you may want to remove the financial incentive and custodial motivation for these fights by termination of parental rights. In most states this removes support, but keep in mind what you are really doing when you file this court action for TPR.

Children who are siblings of divorced parents always eat dirt in a custody fight, and it takes two people to make it work and one to always ruin it. So if you find yourself paying to protect your child from the ex's dirt issues, you may want to file TPR to force the irresponsible party to pay for their own dirt making.

Child support depends on what your two lawyers agree.  Time you spend looking after your own child should have been taken into account.  However, if you just have for weekends I find the mother usually ends up paying for the clothes and food for most of the week plus school trips.

Yes. You should get a calendar & use it just to keep up with the exact times & days the kid(s) are with you. You will have the info for your attorney & for the judge to see also.

Yes, she can