Surface Pro 12 battery drains when shut down

I bought a Surface Pro 12 last December and it has 2 problems (possibly interlinked) since the start. The first is that when it is shut down, the battery drains. Within 48 hours, 20-25% has usually gone. To try and fix this I have:

1. Changed power settings to ensure that pressing buttons means shut down (closing keyboard/lid = sleep but I never close those til I've seen all the lights go out)
2. Performed a factory reset from cloud and run all updates. I did not reinstall all my apps, just my microsoft onedrive.
3. Performed a hard shut down holding the button down
4. Completed a commandline shutdown using /s/t 0
5. Generated a battery report which shows the battery is in good nick
6. fiddled around with the UEFI settings (toggling on, reboot then off again or vice versa)
7. Have disabled fast start up.

Nothing works, the battery still drains. Does anyone know what this may be and how to prove it, more importantly how to fix it. My lovely 1st line support guy at Microsoft is ready to ship it to engineers to take a look at but before anyone else does anything, I want to see if we can fix it... especially since there's no indication of a hardware error (as far as the OS is concerned, I know I know...). that call is on Monday 31st so if anyone could answer before then.

Now just to add the second issue (because I have a hunch it's related to the first). When I boot up, the surface pro doesn't connect by Wifi to anything. I have to do a start, reboot to get it to connect. It will mostly connect to my wifi (the first wifi it ever connected to) but for every other wifi, hell no.

My instinct says something is preventing it from fully shutting down.

Many thanks in advance