If we're taking bets, my call: May narrowly survives the no-confidence, refuses to resign...

[Recursion]

... and the Queen prorogates Parliament

[Doodley]

1. She will survive. No resignation.

[melm00se]

2. When was the last time that the

Crown exercised that power?

[Recursion]

5. I believe Cromwell was involved (nt)

[gratuitous]

3. I don't know about the sequelae

But I think you're right: May narrowly survives a no-confidence vote, but only because there's no alternative for her party. Nobody's waiting in the wings or chomping at the bit to step into the PM's shoes. This is a horrible political situation with no escape. And they brought it on themselves. There would be some grim satisfaction in it, but the ruling party in the U.S. seems determined to replicate the Tories' blunder.

[VMA131Marine]

4. This is a Conservative Party leadership challenge

The Queen would not get involved even if May had lost.

A successful no-confidence vote in Parliament, on the other hand, would result in a new election.

[Recursion]

6. The Queen theoretically may prorog at any time

Just like she theoretically may refuse assent to any law.

[VMA131Marine]

7. Prorogation just ends the current session of Parliament

it does nothing to change the ruling party or the PM.

The Queen no longer has the power to dissolve Parliament (and thereby force a new election).