How is the flag marked as helpful?
When a 3k user votes to close and chooses the same reason, your flag is immediately marked as "helpful" and dismissed. If you choose off-topic → Blatantly Off-topic when flagging for closure, it will match any reason in the "off-topic" sub-menu.
If the question is finally closed, all pending flags, regardless of their reasons, are dismissed as "helpful". Additionally, any very low quality flag will also be dismissed as "helpful", and if there exists at least one, the Community user will cast a downvote on the question.
How can it be marked as unhelpful?
If the question receives 3 "Leave Open" reviews before anyone votes to close it with the same reason as you chose, any pending flag is marked as "declined".
If your flag has previously been marked as "helpful" (by someone voting to close with the same reason), it will remain "helpful". Dismissed flags never change.
How do other (high-rep) users see and vote on it (are they notified when a flag lands in the queue)?
They don't see the flag, nor are they notified. You flag sends the post into the Close Vote review queue, if it hasn't already. 3k users then do the reviews and decide whether to vote to close. When reviewing, they can see a dialog telling them all reasons that have been voted or flagged as.
Is there a way to check how many votes have been cast on it?
With 250 rep, you see close votes on your own questions. With 3k (500 on beta), you see close votes on any question. You won't see the number of close votes on others' questions without the "cast close & reopen votes" privilege.
In short, you can only see the close vote count on questions that you have the privilege to close.
Do moderators handle vote-to-close flags?
In most cases, no. They are handled by the community via reviewing. Moderators can, however, opt-in to review the CV queue to handle those directly. This is not often the case because mods' votes are binding, and deciding whether a question should be closed require specific expertise in the subject, which means people with special knowledge may do better than mods.
If the post have been closed and reopened for several times, soneone will raise a mod flag explaining the controversion.
What happens to the "helpful flag" status if it expires?
Flags that are dismissed never expires. A pending closure flag expires when all close votes expires, if they do not mark the flag as helpful. If there's no close votes, a close flag expires after 4 days or
14 days, depending on the question's view count. More information here. An expired flag has "aged away" as its status, and is technically the same as dismissed.