- Within what time period is the request handled?
It depends. The average is several hours, I think it was about 3 hours last time this was discussed. But there is quite some variance. Also recall all moderators are volunteers.
- Will the moderators inform you by email about their decision?
Normally, not. However, the fate of your flags can be seen here
https://math.stackexchange.com/users/flag-summary/30735 (only works for OP)
You can navigate there by clicking 'helpful flags' on your 'activity page,' too.
There is "pending" (not handled), and "helpful" or "declined" (and "disputed") for handled ones; and possibly custom additional details as information about the flag.
- What are your options if the moderators decide not to take action, and also choose not to inform you about this, thus leaving you in limbo?
It is quite rare that flags are not handles for an extended period of time. It is not rare that no action is taken for one reason or another. This is usually knowable from the link I gave above.
A thing you can do is ask in the Math Mods' office
In severe case, you can also follow the "contact us" link at the bottom of the page. But this will rather get you in touch with SE staff not per-site moderators.