I didn't notice it myself, but I remember reading on Reddit that from some screenshots (the documentation that Elliot got handled by Price) the machine was revealed as a Large Hadron Collider and that it was either meant for alternate realities or travelling back in time.
It wasn't spelled on the nose, but I guess if one really wanted to know, the answers were there, it's just that it was not important
per se what the machine was doing, more what Whiterose
believed it could do, and therefore it was important to her and her motivations.
It's kinda like the prophecies in Harry Potter.... they were bullshit, but Voldemort believed them, and so he made them real. Same here, Whiterose's machine was just the deranged impossible project of a lunatic, the point was not if it worked or not, but that Whiterose believed it would work.
About Tyrell... yeah, that was actually his BSOD
his exit could have been handled better but he needed to be out of the picture to stall the Deus meeting.
Good call on Elliot not knowing Price was Angela's father.... the only one who knew was Angela herself and she got offed immediately after. Let's call it a lucky guess or rationalization by the Mastermind but yeah, he shouldn't have really known.