No, unfortunately, this version of Ep2 v16 (with Bardie) is kind of "outlaw" and those 3 non-critical bugs of Ep2 v16 that we know are not fixed there and won't be fixed. However, full version of Ep2 v16 without problems is passed, and these bugs are insignificant and may not even show up at all during the passage (depends on various factors).
Regarding the save files, I don't the next episode 2). But ifu played in episode 1 you should have no problems with moving the save file to the full version (if you follow the official walkthrough). However, I know that there is another version of the 1st episode where, as far as I know, the developer fixed some non-critical bugs and added a gallery. Maybe this "new" version of Episode 1 is only available on Patreon and if you played that one, there's a good chance that you can't transfer the save from this updated version to Ep2 v16 with Bardie.
As for transferring a save from Ep2 v16 with Bardie to Ep3, that shouldn't be a problem. Most of the "old" players played this classic scheme and everything was fine. Episode 1 ("old")--->Episode 2: New Life (Ep 2 v16 with Bardie) --->Episode 3: Crossroads.
p.s. On rare occasions, individual players will get an error when transferring a save file from ep1 to ep2 (even if they've done everything according to the walkthrough). I haven't had this happen, but I remember someone mentioning it here). In any case, Episode 2 (both with and without Bardie) has a mechanism built in by the developer that allows you to immediately start the New Game and then take a little survey of how your Monica behaved in Ep1. Also check out the
FAQ it will remove a lot of possible questions.