I'm not British, but I'll give it a shot.

May is Prime Minister not only of England, not only of Great Britain (the island shared between England, Wales and Scotland), but of the United Kingdom of Great Britain and Northern Ireland. And that last part is the trickiest one when it comes to Brexit, due to the complicated status of Northern Ireland which is part of the United Kingdom but also has special ties to Ireland, as a consequence of the peace process in the 1990s that ended the Catholic-Protestant conflicts of the preceding decades (the Catholics wanted to join Ireland, the Protestants wanted to remain British). That works a lot better when both Ireland and the UK are both in the European Union; with the UK leaving the EU, there are endless headaches about maintaining Northern Ireland's ties and open borders with Ireland, as the Catholics want, while also maintaining Northern Ireland as an integral and regular part of the United Kingdom, as the Protestants want.

And since it so happens that the handful of Northern Irish Protestants in the British Parliament (the DUP party) are needed to give May a majority of the seats, they have a lot of power - 10 seats vs 316 seats for May's own Conservative party, but since you need 322 seats for a majority, those 10 hold the balance of power.

Scotland is strongly pro-EU and anti-Brexit too, so the whole thing also risks pushing the Scots towards a new attempt to secede from the UK (and then rejoin the EU).

I would guess not, because there are no plausible alternative candidates and anyway her party members are smart enough to realize that this is a terrible time to tear the party apart in a new leadership contest. That leadership contest might still happen nonetheless, but if so she'd win it. For now.

A complicated compromise which, like most compromises, doesn't really appeal to any side. Basically kicking the can down the road and committing the UK to remain tied to the EU in many ways for the time being, until everything can be fully negotiated.

Both sides, remainers and Brexiteers, can kind of agree that in the short term it would leave the UK worse off than it was as a full member of the EU, because it would remain subject to many EU rules or regulations without actually being involved in setting those. Temporarily, of course, only until the future relationship has been fully agreed upon, but who knows how long those negotiations will take or how they will end exactly. And due to the thorny Northern Ireland issue, the UK couldn't even unilaterally decide to end the arrangement whenever it wants.

The problem is that at this point, pretty much the only alternatives are either to reverse Brexit (through a second referendum - though of course, that referendum might not yield the hoped-for result), or to leave the EU without any deal at all. Which would create a LOT of problems in the short run, and only a minority believes it would be beneficial in the longer run.