Yes, Labour still say they're trying to form a minority government, but it's unlikely, and it would be a genuinely minority government. It would seem virtually impossible for Labour to do a deal with the DUP - the DUP are further to the right than the Tories. Their glimmer of hope, however, is that the DUP might refuse to do a deal with the Tories either. In that case, there can't be a majority (I guess Tory+SNP is a theoretical option in the short term if the Tories were willing to give massive concessions, starting but not finishing with an independence referendum, but it doesn't seem likely). In that case both main parties will be looking to form a minority government.
It should be explained that there are sort of four different 'levels' of majority here:
- outright majority, one party has more than half the seats;
- coalition, where a big party gets over the threshold in a formal agreement with another party (who get to have ministers, etc)
- "confidence and supply" - where a big party relies on a smaller party in a semi-formal agreement whereby the smaller party promises to vote with the big party, but only on votes of no confidence and the queen's speech* ("confidence") and on the budget ("supply" (of cash)). If a party has enough votes on confidence and supply, they're the government - but they may not be able to get any other substantive measures through
- vote-by-vote survival - where a big party declares itself the government, and persuades people to vote for it in confidence and supply votes, but on a vote-by-vote basis, and not necessarily the same people each time. This is obviously the weakest position.
It seems overwhelmingly likely that there'll be a Tory-DUP alliance, but it probably won't be an official coalition, but just a confidence and supply situation. However, if the Tories can't reach an agreement with the DUP, the other parties could conceivably unite to allow Labour to function as a minority government, though this would be incredibly unstable.
*every year, the Queen gives a Speech to Palriament, written by the government - basically a 'state of the union'. It lays out the government's priorities and specifies some bills they want to pass in the following year. It has no practical importance, but it's taken as symbolising a party's ability to get their platform enacted. So the vote in parliament on approving the proposed official parliamentary reply to the speech is considered to be a motion of confidence - lose that and you're not the government anymore.
As for May... well, the Tories are incredibly pissed off with her, and some are even saying it publically. The Sun is blaming her aides, and I'm sure that after this and the London mayoralty there'll be a lot of scrutiny of Dead Cat Crosby too.
But the BBC say that they're hearing that, after some uncertainty, it seems May will "survive the day" at least. There's no obvious replacement - Boris is rumbling, but I don't think there's the appetite for him yet - and if there is going to be a new election very shortly, they don't want to be without a leader going into it. So May will probably still be PM tomorrow. However, unless she starts performing miracles she will not survive as leader until 2022 now - they'll let her take the hits over this difficult period, and when things settle a bit they'll replace her. Effectively this election will be the starting gun for the various Tory hopefuls to build their case for the inevitable leadership challenge in a year or two.
But the river tripped on her by and by, lapping
as though her heart was brook: Why, why, why! Weh, O weh
I'se so silly to be flowing but I no canna stay!