I am building a detached drum studio in my garden, outskirts of London, UK. It is residential area so main problem is to reduce the sound as much as possible. There will be 7m gap in between the building and our house which is next to the neighbour's house. Behind the room there is a concrete wall, parking behind it and park, so that is not a problem. I checked planning permissions with the Council and I have to respect some restrictions (height max. 2,5m for example). Sound quality inside at the moment is not a priority, I might use the room for recording one day, but mainly it will be drum/guitars practice room in the first stage. Therefore I'm not worried about acoustic panels and difusers yet, there will be time for that in the future. Now I am worried about making it as soundproof as possible - our drumming should not bother neighbours. Noise coming from the outside to the room is not an issue - it is relatively quite place here.
I attach 2 sketches - sorry that it doesn't look professional yet, this is what I got at the moment. It will be room within a room construction, external walls 550cmx490cm, height 250cm. Walls made of 6inch concrete blocks (outside) and 2-3 layers of 19mm plasterboard with green glue (inside - both walls and ceiling). Inner walls will be built on Neoprene panels. I got already foundations and screed separated by 5cm styrofoam (so vibration of inner room are not transmitted to the outer one) and we're starting to put external walls tomorrow. No windows, two heavy, steel security doors back to back (one in each wall). Flat roof made of two OSB's with insulation in between joists, fibreglass outside and MLV (Mass Loaded Vinyl) from the inside. Of course we know it should be airtight so we will try to make it as tight as possible, we will use acoustic sealant in all corners etc. The HVAC system to be planned a bit later. At the moment I need to focus on buying right materials and explaining how to use them to my builders - as you can tell this is not my profession, I'm not even DIY type of guy, I am musician thus I need some help of yours!

I would really appreciate some assistance with a few questions/design problems I have:
1. I have 20cm gap in between walls, what is the most efficient way to fill it? Rockwool and air gap, Rockwool and MLV , just MLV, something else...?
2. In between drywalls should I use Tecsound or Green Glue? In theory GG should reduce lower frequencies more as far as I understand that, but maybe I am wrong? Any other options? Is it enough mass?
3. What should I put in between concrete screed and drum carpet - more MLV? 4. Is there anything missing (apart of the HVAC - I am aware of that) in my plans, some big problems I can't see yet and you can...?
I will be grateful for any assistance offered,
Karol