[Legate of Amon Lanc]

Well interesting questions... I think these could be answered in many different ways, but let me start from the end.

At least with Manwë and Melkor, they are said to have been "brothers" in Ilúvatar's mind and it seems, more or less, that they were on a similar level. However, Melkor is said to actually have been possibly even more powerful than Manwë, sharing pieces of power of each of the other Valar. So in this respect, I would actually think it would have been "easier" for the folk in Middle-Earth had Manwë and Melkor switched places, it would have been far easier to overthrow Manwë (and on the other hand, Melkor would have been a far stronger opponent for him). The only advantage for Manwë I could imagine will be that at one point, he would have achieved total "air supremacy" in Middle-Earth, which would result in general spread of agoraphobia. The skies would become feared, as basically at any point you'd be travelling across some wide plain, something big will come upon you from above. Also, Hitchcock's "Birds" would definitely come to effect... eurgh.

The main "advantage" Manwë had against Melkor was his closeness to Ilúvatar, which, of course, he could not use in this scenario. In order to turn evil like Melkor did, Manwë would also have to become arrogant corrupt fool, like Melkor and Sauron did, that means, getting this "overlooking the obvious" syndrom (like becoming too full of himself and as a direct result of that, becoming defeated - as in overlooking two Hobbits in Mordor).

And for the first one, I am certainly convinced that Sauron would have the power to conquer Middle-Earth, as that is said many times. The people at least could not stand against him with force: eventually, they will be defeated. One Gandalf or even Gandalf with Aragorn restored could not save the day. The only remaining chance would have to be a help coming from overseas, but since Valar forbade themselves from assisting directly, not sure how would it be possible. If the situation was dire indeed, they could ask Eru again for a permission to do something (like to send an army of Istari), theoretically, yes, but at most that will be the Last Alliance all over again - I think the point was that the peoples of Middle-Earth need to get rid of the Ring by themselves.