For example
On other torrent programs I can see the files of other users who are downloading from me, or me downloading from them. That way, if they have a fast connection, I can check for more of their files and see if I want other torrents they already have.

Is it possible on Tixati?

Tixati doesn't do that. I wouldn't like to show all my transfers to anyone connected.

If you join one of the "channels" for chat...

You can click on a user in chat and "browse" for what files they are sharing.
Or once you join a channel you should be able to use the "search" tab to search peoples files in the chat channel you joined

Only works for other users in channels/chat

Which torrent clients allow you to browse other peers' files? I've never heard of this before.

You can browse the files of others only if both of you use Tixati.

I think there is a basic misconception about browsing and share lists in tixati.

Yes, a user can make a list of .torrent metadata files or magnet links. But that is all it is...a list of links that you are browsing. A user can show 10,000 links but not have ANY data content at all for those files and might not even be sharing any of them.

IOW, seeing a file when browsing a user is not evidence they are uploading or downloading the torrent or even whether or not that user even has the content of the torrent. So you are not seeing the actual media files that user may or may not have.