Has anyone been to Tbilisi Airport?
Yes.
Whats the lounge like?
Nice enough. It's a little way before the gate and I think just before security (if I recall correctly). There are drinks and some snacks including nice looking cakes. There's a computer to use and read materials. It's a modern airport with a modern lounge.

Duty Free worth a visit?
Probably not. I think they're generally more expensive than the local shops in this part of the world. I'm willing to be corrected though.

- The first leg to Baku is scheduled to take 1h 15m, will anything be served?
Just 'Your choice of drink'.

Are loads light from TBS, then the flight fills up from Baku?
Not in my experience. It's about half and half I'd say.

- We are meant to be in Baku for 45 minutes - I assume you have to stay onboard?
Stay on board.
Or is there a choice?
No. And you are not allowed near the door/galley area during this time.
Or is disembarking compulsory?
Nope
- The second leg is scheduled at 6h 20m (dep 1140, arr 1400, 4 hours time difference), will there be just one meal, or also another snack before landing?
It's just the one meal, no snacks.

- Can I get access to the Star Alliance arrivals lounge? I know it is meant to close at 1430 so unless the flight is really early (which it is on occasion) I won't get in anyway.
You will be unlikily to get in unless your flight is very early.

OT, Why is Tbilisi 12,000 miles for a redemption, but Baku 40,000? Works out well for me, but makes zero sense. I suppose this is DC....

The flight used to make a stop in EVN which is also zone 2. Now you wouldn't want them to give DC any ideas would you...the extra segment does make the flight a bit of a pain so I like to see it as some sort of payback. You may notice that you actually fly over TBS airport from LHR-GYD vv. albeit at quite a height.