Yes. If you are have been already admitted into the United States, all you need for domestic travel is your passport.
Yes there is regular flight service.
Yes, it is.
fly
you can be any age
Yes, if you have an Irish one.
No , you do not need a passport unless you are leaving the US.
About five hours.
it takes about 5 hours to 5 and 1/2 hours to fly from Florida to California
A passport is not needed to fly from one US state to another. However, you will need a photo ID of some sort to board the plane.
If coming from the US, Canada, Europe or Japan, all you need is you passport. Otherwise, you will also need a visa issued by the Mexican government.
Yes, passports are required on flights between most countries these days.
Hawaii is a US state - if you don't need a passport to go to Nevada or Michigan, you don't need a passport to go to Hawaii.
Your question is a bit misleading, but yes you could travel from the US to the Dominican Republic with a Mexican passport. In fact many people need to make such kind of connections as Mexico doesn't have direct flights with many countries; one instance would be Portugal: Mexican tourists have to fly to the US, Spain or the Netherlands to reach Portugal.