I live in the U.S. for the last two years, I came here on B2 visa. My status has expired due to some problem before. But I still have my passport. Can I still fly a domestic airline from Boston to Dallas or any other airport in USA with my passport? Would there be any problem?
Not at all.
Flying within the US has no border control (makes sense, as you are just flying within the same country).
All you need is a TSA approved identification document.
Immediately after 9/11 I was flying from San Diego to Dallas, and I was carrying only my Texas driver's license (and no passport).
I was approached by FBI, airport police and INS officials at the airport for some enhanced security checking (keep in mind, this is before the TSA existed in its current form).
They asked me for the purpose of my trip (I was visiting a friend), why I had a bag of quarters in my carry on (we had been to an arcade) and a few other questions.
The INS officer asked for my passport and I told him I don't carry it with me as I do not need to while traveling within the US.
They asked how could they prove I was legally in the US. I had my university fax them a copy of my passport (as I waited with them in a secure area of the terminal).
That is the only time I have encountered such scrutiny (and keep in mind - that was an exceptional case due to the timing of my flight and the obvious security situation).
These days, for domestic flights they just need to match the name on the reservation with some form of ID.