I currently have 1/2 custody of my children. Can I give up that 1/2 custody without my ex contesting it?

You need to file a petition for modification of the agreement. And, if its a job that paying more, i believe the court will grant you the request...

Can i file a lawsuit for sexual assault?

No you cannot sue for sexual assault.

Violating an order of protection??

It appears to me from your post that she has violated the order of protection. Call the police and have her arrested

International sue due to a domestic case

Absolutely, she can file a civil law suit against you.

I was rear ended by a car that rear ended me. The driver in the first car ran from the scene. I suffered a back injury.

The statute of limitation is three years, so your are within the limit because the accident occurred in 2013

Absolutely, camp and extra curricular activities are part of child support.

Can I file child support in NYC if I moved to Texas, and the father lives in NYC ?

Certainly, Ny still has jurisdiction over this matter. The child has not been in Dallas for 6 months and the father still resides in NY.

If custodial parent has taken child out of daycare does it make sense to have child support reviewed for downward modification?

Yes if the money that is given to the custodial parent is for day care and the child is no longer in day care file for a downward modification

I currently pay 25% of my income to child support. My current spouse is not pregnant. Does this reduce a current support?

absolutely not. You child support will remain he same, so sorry

What will I likely get for support, legal fees award?

How many children do you have, If you have one child its 17% of his gross income. As far as for spousal support i need more information. You need...