It is not Dishonored.
A small (probably coastal; at least it has a port) town, no idea where. It's governed by "some" (going more into detail might be an instaguess hint) holy order which is led... or should I say "was led"? by an elderly priest who recently got a bullet where it didn't belong.
At least partially, yes. That's the reason he managed to survive those encounters (first with the assassin and then the one where he discovered the truth about the priest) while most people wouldn't make it.

Is it a Gabriel Knight game?

No, it's not.
This one has way more slashing.

Is it an RPG?

No, it's a slasher. Of a rather well-known series, I might add. :-)

Blade of Severance? Or is it something more modern? I haven't played many of those.

No, something more recent. Although even this isn't the latest game in the series.
Fun fact: if you bought a bundle of this game and its predecessor in Steam, it actually cost less than the previous game of the series alone.

Darkstalkers II?

Edit: Actually, that's probably not it. Can you describe how does the protagonist look like? What his favourite foods are?

No. Not even if you meant Darksiders. :-)

Since I've already told there are more playable characters than one, I'll describe the one you start the game with. He's a young man in his early twenties (I think), white hair, blue eyes, wears a red jacket, dark blue coat and pants; one arm in bandages (initially). No idea about his favourite foods, he's never shown eating.

Yep, Devil May Cry 4 starts with Nero nearly being late for Kyrie's performance, then Dante shoots the old priest and the fun starts. :-)

Your turn.

OK my team have so far busted out of prison, rescued / recruited another team member and are now trying to 'obtain' fake passports from the Lebanese embassy (or is it a trophy I'm purloining? The game seems a little confused on this point...)

Monaco! Right? :)
But...but...dang! You're right! :D I just associate DMC more with Dante than Nero.

Yep - Monaco - your turn!