1. Probably the references are to the "clean the monsters out of the sewers" jobs you can get from mayor types in GH1. You have a better chance of getting one if the mayor likes you.
2. You've been trying to take down everything using
Mecha Fighting?

Oy vey. Yes, there is a "fire projectile weapon" key. Do the tutorial in Hogye in GH1, and check the menus and the help.
3. The last time I played a character with Performance was in a much earlier version of GH1. But I'm pretty sure the games don't have the same limits on it at the moment—GH2 is once per game-day or once per day per spinner or something.
4. In GH1, the Argoseyer beats most other mechs hands down, especially with a bit of tweaking. GH2 I'm not sure about, and it'll probably change with the next version anyway.
5. To be able to tackle tougher missions, your character needs strong mecha distance combat (Mecha Piloting, Mecha Weapons . . .) and personal combat (Dodge, Armed Combat . . .) skills. Put your experience into the mecha skills at first, though, and let the personal ones take care of themselves for a while. In GH2, the Conversation skill is also vital—without it, you won't be able to get missions. GH1 offers some introductory missions and a first dungeon (Hogye Mines) to get you started. GH2 offers you an initial mission too, but it isn't really balanced yet and you may find yourself getting creamed. Also, cyberware is a good way of raising your stats in GH1 if you have the Extropian or Cyber-Psycho talents (in GH2 it's more of a crapshoot).
Do the GH1 tutorial in Hogye. Read the Guides section of the wiki:
http://gearheadrpg.com/wiki/index.php?title=Guides. Above all, have fun!