What you do on other websites won't effect your ban on outpost. So long as you aren't scamming users.

You wont get marked for it, but its recommended not to do the trade with the user.

According to https://steamhost.cn/steamcommunity_com/groups/tf2outpost/discussions/0/618457398962081568/#c618457398962081468

Its been like this for a while, the info is cached every 20 minutes or so.

This is a problem with the Steam API, the site is limited to the amont of times it can check users profiles a day. So it's basically impossible to get real time info on user accounts. Just check their profiles and act accordingly.

Once someone offers you a trade, you have to add them on steam (the plus button in the top right of the comment) and trade them from there.

https://steamhost.cn/steamcommunity_com/groups/tf2outpost/discussions/0/558747922562007365/#c540742485382216907

https://steamhost.cn/steamcommunity_com/groups/tf2outpost/discussions/0/558747922562007365/#c540742485382239358

I think this ban was totally justifiable, considering you bought an unusual for an insanely low price. Without any proof of course it's going to be considered a shark.

https://steamhost.cn/steamcommunity_com/groups/tf2outpost/discussions/0/558747922562007365/#c540742485382216907

In the report function you can set the reason to "there's something else" use that option.
https://steamhost.cn/steamcommunity_com/groups/tf2outpost/discussions/0/558747922562007365/#c540742485382239358