The same flight number may be used for multiple flights each day, or different flights on different days.

IAH-MIA "should" be on time, it's too far south for snow, and too early in the year for thunder-bumpers.

The bag will fit but they may want you to gate check it. If you board late and the flight's full they may run out of bin space and then you'll have to gate check it. But you'll get it back planeside immediately after you arrive.

I'm not flying it.