Is there shooting PCs?
Is there shooting NPCs?

Shooting PCs (and player-owned NPCs) is in beta on Derra only, but as it is in beta it can only knock you to 1 HP and cannot kill you currently (but can kill the player-owned NPCs).

Randomly spawning bandit NPCs can be shot to death anywhere in the galaxy, along with creatures.

Thank you sir.

Where nay I find a gunstore on Tatoonie?

A list of NPC shop locations is on this rules page. You can buy basic items, droids, weapons, and armour here (full list of what's available and the prices is a bit higher up on the same page).

If you want better gear than what is available at those NPC shops, you will have to interact with other players and factions to purchase them. You can contact the relevant item factions directly, browse the Commerce forums for people selling or look at offsite markets like CentrePoints Market. However most will require you to travel to their location to pick up with not many giving delivery.