The TSA checks passengers' identity and whether a passenger has a boarding pass; generally, they are not screening for immigration status.
People Also Ask
Yes, as noted above, the list of approved identification to fly domestically includes foreign government-issued passports and/or a U.S. Citizenship and Immigration Services Employment Authorization Card (I-766).
You'll get through customs in a couple of minutes (unless you are stopped for extra checks). It's immigration that can take time. If you have booked this as a single ticket and you meet the minimum connection time then the airline is responsible for getting you on the next available flight at no extra cost.
Removal or deportation orders stay in your immigration file forever, so you are for example seeking a tourist visa after the 10-year bar has passed, you need to be very forthcoming and explain what happened and how the situation has changed.