I Don't think so? I've never tried. My guess would be no.

I've heard you can transform into a mega evolution by copying a mega evolved pokemon, but I've never tried it.

No. You can copy any mega evolutions but the game registers Ditto as Ditto, regardless of what the model is.

From my understanding, no. Obviously, Ditto does take the form of a Mega evolution if your opponent has already evolved, but holding a stone with Ditto doesn't give you the option to evolve from the base form. Haven't tested this myself, but others have confirmed it.

So getting an Imposter Ditto that you send out after an opponent has Mega Evolved would totally be a viable option though...

Yup. Unfortunately, switching takes priority over Mega Evolution, so you can't swap Ditto into a normal Lucario even if it Mega Evolved on the same turn. However, switching into a Mega-mon that has already evolved is fair game.

Although, come to think of it, normal Mawhile makes a pretty good counter to Mega-Mawhile thanks to intimidate.