Only one ship is sailing out of Tampa right now, a Carnival ship.
She's due back in Thursday, though I'd be shocked if those folks don't get a bonus day at sea.
Since tomorrow is a sea day anyway, they can take a cautious approach to see where Ian actually goes. If it goes as forecast then Liberty could probably go with its original itinerary.
Sandy passed about 90 miles north of where I lived at the time, but the cold front coming in mitigated any real bad effects. My worst experience was Tropical Storm Lee which dumped 7" of rain and flooded a window well into my basement.
It's not really a matter if they can take off as much as it is them not wanting planes (and maybe more importantly crew) getting stranded there for multiple days. With a big storm coming in airlines often pre-cancel flights and move their planes elsewhere.
That said MIami should be OK.
The issue isn't covid itself, but still the overly strict protocols crew have to follow if they test positive.
Some probably fear some retribution if they get covid without a mask, regardless of what the individual crew member actually thinks of mask effectiveness.
That said I would imagine most crew have gotten covid at one point or another anyway.
There's no way to give a true boarding time since there's no way to know when the ship will be cleared for boarding or what kind of lines there will be once you enter the terminal
If it's your national vaccination proof, you'll be fine.
As for the test, just go buy a cheap at home test at a local pharmacy once you get in the states. That's all you need now.