No, the House has to pass the Senate version FIRST, and then fix any problems that the House had with the Bill with Reconciliation.
And the reason the Senate version can't get passed in the House is the abortion funding issue-which Reconciliation will not address.
No, they don't. So long as the President signs the original bill first, theirs no conditions about what legislation has to be passed first. They'll pass Reconciliation in both Houses of Congress and hold it from the President (they can hold a bill for a year before it expires), then they'll pass the original Senate bill in the House.