Captchas are primitive wastes of time, can't argue with that. Apparently the staff here doesn't "get it" but then again a lot of other websites are still using this "feel good" "security measure"
https://www.scientificamerican.com/article.cfm?id=time-to-kill-off-captchas
As for your other problems since you didn't describe your OS, browser, hardware or ISP I guess you're not interested in doing anything besides assuming it's all chess.com's fault (maybe it is, then again maybe not) In case I'm wrong click on this link for some general troubleshooting tips and fixes:
http://www.chess.com/blog/NimzoRoy/diagnosing-and-fixing-internet-problems?_domain=old_blog_host&_parent=old_frontend_blog_view
What a terrible site....played three games this morning all three were ended by loss of connection ..won 1 lost 2... little green box full... browser and wi-fi connected . Seems Chess.com servers are not fit for service. I paid good money for this site...then to cap it all I cannot submit a complaint because it says my captcha entries dont match... no help is available , I assume spaces are sensitive is are caps ....what a waste of a saturday morning.