[1] Of course, you still have to give two weeks notice if you want to exercise that at-willness for yourself!
[2] I mean, unless he "randomly" fires all the people of race X, or something like that
Tom has spent considerable time (as I have, in my own company) getting people to a point where they think for themselves, make decisions as a group, and generally behave as independent adults rather than the kind of infantile employees who just do what they're told by their boss. Since the latter is the way most businesses operate, it's no mean feat to get this done with a company of a dozen, let alone with one of hundreds.
If Tom decides to arbitrarily fire someone, even just one person, without going through the group-oriented processes he's spent all this time building up, he immediately undermines all that, potentially fatally.
Since he clearly cares about the company's culture (enough to make it his priority for the last half-decade), it's very unlikely he would risk that to get rid of one person.
And finally, again, there's the evidence: if he really did want to get rid of this woman, and he could, why didn't he?
That's more speculation than evidence, surely?
No, you don't.
That's a professional courtesy; it's almost never legally required.