Not an expert but I'll try...
@ihcob said in #1:
> I've read in the past that in the Italian White looks to play Bb3 to preserve their strongest piece once ...Na5 becomes a possibility, but lately (for example in the SCC broadcasting while I type this) the strong players just let the Bishop chill on c4 very late into the game...
This IMHO depends on what black plays. Normally, Na5 is not much of a threat because the bishop can be moved into safety via the b5-a4-c2 dance (and there is also the option of b4 counterattack if black bishop is on c5). Once black plays a6, though, white loses this path so that Bb3 is often played in response to a6.
BtW, it's interesting that the h3 and a6 moves are often played in Italian (especially the "Modern" variant with c3-d3), even if most coaches hate these moves otherwise (when played without a good reason): black plays a6 to drive the white bishop away from c4 and white usually plays h3 to prevent Ng4 response to Re1 (played to prepare the Nb1-d2-f1-g3 transfer).
> Also after ... Be6 I've read that White should only play Bxe6 under very favourable conditions, but I'm seeing GMs play Bxe6 very often, with both ...fxe6 (which seems to give Black a strong centre) and (to my surprise) ...Rxe6 in reply.
That's a hard question. It seems to depend on position and also on player and his/her plans and personal preferences. Some players prefer the e6 trade, some rather hide the bishop on c2 even if it looks quite passive at the moment. Personally, even if I decide to allow the bishop trade, I prefer not to do it myself (by Bxe6) but rather let black trade with Bxb3. The reason is that fxe6 opens the f-file so that the black rook can be quite troublesome and at the same time the e6 pawn supports d5 which is then kind of inevitable and harder to deal with. And the white rook on semiopen a-file after axb3 can be quite handy later. But as I said, I'm far from an expert, rather an enthusiast.