It's always a good idea to check up on the WineHQ page for apps you're trying to run in Wine, they often have tips, tricks, or at least bug reports about little problems like this.
The WineHQ page for Team Fortress 2 might mention at least one of your problems:
Team Fortress 2 is Dark and doesn't show the menu correctly.
This bug is related with the last Team Fortress update and some nvidia video cards, you can solve it by adding -nod3d9ex at the launch option into the game, to do that, right click at the game on steam, go to Proprieties and click into Set Launch Options.
As for the font issues, it's been a while since I last played TF2 under Wine, but the fonts were always not quite right; it wasn't that any were missing, but they all got (understandably) rendered a little "off." TF2 should come with its own fonts, especially since what you say you're missing is one of the more unique comic-style fonts.
Of course, Steam's "Verify Integrity of Game Cache" under a game's Properties → Local Files tab is always worth a try if you can't identify any other problems.