I've read that Huber clocks began using lantern pinions with pin pallet movements after a patent expired (DRGM 502714) in early 1915. Given that the war was going on, likely your clock is dated to shortly after WWI.
As for polishing the brass, I'm sure a few others will chime in with their methods. The base on your clock is quite tarnished with the old lacquer having turned colors. To cut through that I would probably try using acetone but be careful with the fumes and do it outside. If the base has an internal piece of wood for stiffness, be careful it doesn't soak up the liquid. On tough cases, I've used a gel-like paint stripper. Once I get through that, I use a metal polish such as Simichrome or Blue Magic to slowly polish the surfaces. I wrap a finger in a micro fiber cloth and dip it into the polish past. Wipe on and wipe off! Be sure to fully clean the whole area to get any residue off. This removes the old lacquer so you should follow up with a wax or spraying another coat of lacquer. There was a recent thread on use of lacquer.
Lacquer for brass | NAWCC Forums
I notice that your fork is angled where it contacts the anchor pin. If the clock runs fine, maybe leave it alone. However, this probably requires extra power to run the clock. It might perform better if you were to level the fork out.
Kurt
