Can I travel to California if I have a child support warrant that the rears is over 20 thousand? Also will TSA check my ID to see if I have any felony warrants

Yes TSA will check. Whether you will be allowed to travel depends on whether the agency that issued the warrant wants you arrested.

You may travel if you owe Child support, if you travel to the area where you owe the support and there is a warrant for you, expect to be detained.

If there is a warrant for you, yes the TSA will know. Now, they may detain you, and wait to see if the state that issued the warrant want you returned.
That will depend on how far from their state you are, and what the charge is for.

As a police officer about 1/2 of the people I stopped with warrants, where let go after contacting their home state.