whats the likely outcome for the UK? Will they actually be leaving the EU or is there any hope of them coming to their senses?

so they haven't the faintest idea what the likely outcome is, and since they are nominally the legislators, it's all up in the air.

It looks incredibly unlikely that May can get any deal passed now. Any move for a 'harder' Brexit may get vetoed by the EU, which negotiated with May on the deal. It doesn't seem likely that Corbyn could take control of Parliament and get any kind of exit deal passed, either (for one thing, he doesn't want to get blamed for it). But for MPs to take control of parliament and force a new referendum also seems a long shot. Even less likely for them to just say "we're staying after all". I fear a 'no deal' Brexit is going to happen, because that's what happens if no-one gets their shit together before Halloween.

...(vote for a deal, revoke Article 50, hold another referendum), and there doesn't seem to be majority support for any specifric outcome. If they had held all these votes immediately after the referendum, the likely outcome would be no Brexit for the same reason; however, once Article 50 was invoked by May, the fuse was lit.

The position does involve deciding the business in the Commons, but it's not one of the 'great offices of state' - PM, plus Chancellor, Home and Foreign Secretaries, that are most senior in the Cabinet. It's typically mid-level in terms of power in the cabinet.