On what grounds would they sue for? Email is not the post; there is no legal right to receive one or to have one routed.
If one wants such legal protections, there is the post.
(Now, should there be such a right? That's an interesting question. But a world in which one exists would raise the bar to starting one's own email server even higher).
Possibly, but it would be a hell of an uphill battle. There was no contract in place for the email provider to negligently interfere with. And the email provider's operation was perfectly regular and within the bounds of the standards of that service (which offers no delivery guarantees).
It depends on the circumstances. In some cases, when guarantees are made and those guarantees are broken, you can sue civilly to be made whole (in a context like this where there was no bodily harm, merely an opportunity missed).
It's real unlikely any such guarantees were made. To do so would be extremely foolish for several reasons (the false-positive rate of spam identification is known and emails can fail to deliver because of an error at either end of the transaction).
You can't sue someone (and win) for "this person did something that I don't like". You only have a case if you have a contract with them that lays out specific duties, or if they are otherwise a fiduciary of some form. Unless you signed a contract with microsoft for them to deliver your mail, they have no obligation to do so.
If one wants such legal protections, there is the post.
(Now, should there be such a right? That's an interesting question. But a world in which one exists would raise the bar to starting one's own email server even higher).