On the default’s theme Activity page, rather than the list of activity being paginated, it has a “load more” button. The “bp-activity-oldestpage” cookie remembers what page of activity the “load more” is on.
This might sound like a stupid question, but how do you know that the old comments look like they were posted by you? Is it the same gravatar and user name?
Mercime is very generously giving you pointers to make changes to your theme. If you’re still having problems, you may need to hire a theme developer to help you out.
If you switch to the BP Default theme, do you still get the problem? You can switch back to your regular theme after testing, it just helps narrow down the possibilities.
“MySQL server has gone away” is a pretty important error which must be affecting several things, even if it’s not the root cause of this issue. The connection to your database is being dropped, or lost, for some reason.
I do not know too much about configuring MySQL servers. The relevant documentation is http://dev.mysql.com/doc/refman/5.6/en/gone-away.html — I’d hope that your host would have sufficient technical knowledge to better understand approaches to fix the problem (it’s likely to be a configuration change done on the server setup, rather than your WordPress install).
Anything in your web browser’s javascript console (if you know how to access it) when users reply to a forum topic? Anything added to your web server’s PHP error log? (Ask your host for help if you are not sure how to access that).
