chess.com has become cess pool of bots and automated cheating.
https://support.chess.com/article/648-what-do-i-need-to-know-about-fair-play-on-chess-com
Discussions of cheating, potential cheating, or cheat detection are not allowed in the general forums.
If you would like to discuss, join the following club:
https://www.chess.com/club/cheating-forum
Regarding lag, your opponents can't impact your connection at all since the clients never directly connect and your connection information isn't available to them.
https://support.chess.com/article/213-how-do-i-fix-my-disconnect-lag-issues