Do stores change their merchandise at all without player involvement? I'm rather disappointed at the lack of any weapons/armor I'm actually looking for and at a lack of ammunition for sale.

At least 2 stores I know of will change inventory based on what you do. There are probably many more.

Inventory are unlocked for all stores as you level up. like you will not find an Anti-material Rifle on sale in any store till you have reached the appropriate level.

Do you know if Gun Runners respawns or not? I just want some service rifles to repair my assault carbine as well as an ammunition supply for it and my other weapons.

All stores restock with a different loadout of supplies, generally speaking, you can just wait for 73 hours one cell away from the vendor to get them to restock. Waiting in the same cell can prevent them from restocking since they fail to reset properly with you present.

Gun Runners' merchandise hasn't changed, and it's been over 5 in-game days since I first went there. I'm not sure about other stores.

You need to completely leave the cell Gun Runners is in, and use the Wait command (someplace like Mick & Ralph's or Crimson Caravan will work) for a total of 73 hours in a row. For some reason the timer on them is a bit buggy and tends to kick in mainly on use of Wait or Sleeping, rather than counting overland travel time or fast travel.

Items are level based. You might not be high enough level yet for the weapon to show at shops.

Service rifles aren't anything special.