Can a Gnome Necromancer...
 

... use the same stores as good people? Go to Wood Elf town? Hang out in Freeport bank?

It depends on Bertoxx or not i think, With Bertox as your deity - probably not woodelf bank if im not mistaken, i think you can get into freeport but be wary of bards/paladins?

You can even make a level 1 Gnome necro on Blue and test it out!

I was thinking like getting to HHK and selling at lesser faydar nybright sisters.

No you wont be able to sell or bank in kelethin or felwithe or kaladim without faction work.

There's an evil bank in the freeport sewers and one in the qeynos sewers you can use.

Where is the evil bank in the freeport sewers?

How about ruining your own lands and staying away from mine?

Here's a good video that shows how to get there from the West Freeport gates, starts at the 31:02 mark.

https://youtu.be/vlHBrL_c0tk?t=1862

Gnome necros are pretty safe faction wise except for clerics/paladins. Freeport has a wandering one in one of the zones that nailed me a few times.

Forgot which deity though, but gnomes are pretty neutral with factions, also you tend to be dubious a lot instead of KoS.