Without the support of the DUP the Tories don't have a majority in Westminster. That isn't affected by whether Theresa May, Boris Johnson, or Jeremy Rees-Mogg is Head of the Tory Party.

If Tory rebels got together and forced her hand, or forced her out, there'd be no way to avoid a General Election.

The legal situation in Norther Ireland over abortion is significantly different from in the Republic. Before the referendum no Irish government could legalise abortion even if it wanted to, because of the Constitution. Now we can expect it to legislate to change the law. However a Northern Ireland government can already do what it wants to change the law, without any need for a referendum - but of course, there is no Northern Irish government to decide one way or another.