The first post in this thread also covers the trust level requirements
Note that an ingame account suspension will keep you from getting TL 3 on any characters associated with the account. I believe the intent was to handle posting character disciplinary actions the same way but it appears to be broken.
We are told that forum posting characters are not related at the account level but some display account wide achievement points while some don’t and some people can select among all their account characters for posting, and some can’t.
That has been identified as a bug and all posting characters should eventually be related to your account for everything.
I would suggest posting this question in the website bug report forum which appears to be monitored by the web developers at least periodically.