Also that would be awesome.

Untill the changed gravity pulls the earth more close or further away from the sun, than we will like. Seriously, the circeling of the planets are interconnected and any big change to that, will have effects on earths year length and distance to the sun. But on the other hand, if we would have the tech to "move" mercury around, we probably could also adjust earths rotation. In either way, this is nothing remotely realistically with current state of the art.

Only on the scale of millions of years.

From the little weight alone under normal circumstances, yes, but when the whole system becomes chaotically unstable, then unpleasant changes can happen fast.

That comes later.

First you want to get your self-replicating probes occupying the Oort cloud, whatever. Get ready to sort and aim. You start with your "rocky" bodies, skipping them off of Venus' atmosphere, just ripping it off in big hunks, until you're down to about one Earth atmosphere.

Next, you flat up drop your icy bodies into Venus, because it really needs water.

During that time you'll want to start constructing your insolation shield, to help cool things down.

Only after that can you move Mercury into place.