In the state of Florida, if a father fights to get shared custody of his children, will his ex wife still be entitled to child support?

They may, it can depend on income if there is a large difference. In general these are issues worked out by your attorneys in mediation.

Shared custody is pretty much the normal status for most custody cases. If you have equal time, but do not cover equal expenses you still pay child support. Also like chuck said, if there is a substantial difference in income between the two houses, it is possible you will still have to pay child support.