Domestic Travel does not go through immigration, customs or DHS? Only TSA?

Is this the same at all airports, even international ones?

My cousin and I are planning on travelling from NY (JFK or LGA airports)) to CA either (SFO or OAK airports) round trip. She overstayed her B-2 visa and has an expired I-94 card. Her expired visa is in her old passport but her new passport was stamped stating that the visa is in the old one etc. Can she still travel within the U.S. This trip is very important to us.

Also, she is in school and has a college I.D. Can she use this ID or only her passport?

So what you are saying is your friend is an illegal alien? That doesn't give me much incentive to assist when this site is all about the issues of legal aliens trying to use the system to progress through the immigration procedure

Yes she is but it's not her fault. She came here at the age of 16 and was unfortunate due to the actions of her family who are legal by the way.

for domestic travel you only need a form of identification (such as state ID card or driver's license). She may use her new passport if she doesn't have another form of identification, however a passport is not required for domestic travel.

what a kind way to word what i was thinking.

Its limited to passport or government issued ids, like drivers licenses or military ids.

Its not the responsibility of the TSA to enforce immigration, but if they do see the expired I-94, they could refer the issue to immigration.

They won't see it. Keep it open to the passport page and you shouldn't have any problem. Most TSA agents hardly look at it anyways, all they check for is the date on the boarding pass.