I've had a similar experience with my DGT Bluetooth e-boardm, at least as far as #1 is concerned. In fact I've found it unusable with chess.com.
I wish I had some idea on how to fix it, but it probably boils down to the integration's implementation, which seems to be superior on Lichess.
Hi - glad to see this group!
I have a DGT smartboard that works fine on LiChess, but I have a couple of issues using it on Chess.com.
1) The board sometimes loses synch with chess.com. This typically happens early in the game, say 10 moves in, where moves are recognized on DGT Livechess bot no longer transmitted to Chess.com
2) Chess.com occasionally makes a move when nothing has moved on the board. For example, you are thinking about your next move, and chess.com announces "rook on f8 to c8" making a move when no pieces have been touched.
Anyone else having similar issues or have any ideas about how to fix this? Since there are no issues like this on LiCHess, I don't think this is a problem with my DGT not working correctly.
Thanks,
Carl