Dreamer with a K75 (07/85) in Devon UK

[ManosKoumiotis]

Hi from another dreamer!

My name is Manos and I have for years been dreaming to have a BMW K bike and also of doing my first-ever rebuild (despite not having any relevant experience before).
An impulse search on Ebay about a year ago brought into my hands a K75C dated from 07/1985 with 74000 kms.
The bike was a non-runer for at least 10 years, had 3 previous owners before me, and was imported to the UK from Europe by the first of previous owners.
This was the condition of the bike when I bought it:

[ManosKoumiotis]

The bike was not locked and turning over and was in relatively good condition although quite dirty and with several signs of rust.
She came with a colour that I really liked and two (not) identical tragkorbs. All paperwork was in order.
I loaded her into the rented van and headed back home.

After a few days and a good wash, I had a more thorough look to find that my initial thoughts were not very mistaken and that hopefully, this would be a good basis to work with. 

With a friend's help, the next thing was to see if the cylinders were providing any compression.

The first was ok..ish!

The second almost had no compression!

The third was similar to the first.

[ManosKoumiotis]

The bike in general showed her age and despite being left for about 10 years uncared and exposed to open weather, was in workable condition.

Still, I do not know if I'm a stupid romantic that just wanted to revive this bike by learning how to do it or a complete idiot!
The decision thought had been taken and the first phase involved turning this bike into pieces!

[Laitch]

I do not know if I'm a stupid romantic .  .  . or a complete idiot!

You're neither; you're an adventurer! Lucky for you, your lack of specialized knowledge is unlikely to physically harm you, like it would if you were undertaking your first free climb on the Dawn Wall. 

Keep in mind that when you're running a compression test on a neglected engine, you could be pumping stale, debris-laden fuel into the fuel injectors when you do it so you might want to clean out the fuel tank, replace the fuel filter and replace the fuel tank hoses if you haven't already done that. Furthermore, if the battery cranks the engine too slowly, the starter relay is likely to seize so don't overdo it; keep the battery charged. Compression readings would be more accurate from a fully-warmed engine but since that isn't a possibility right now, the following technique might give you better assessment of what you have.

Piston rings on an unused, unlubricated Brick can seize and lessen compression. Charge the motorcycle's battery. Get some fogging oil. Remove the spark plugs, spray the oil into each cylinder. With the spark plugs still removed, screw the tester into cylinder #1. With the throttle held wide open, crank the starter, and read the highest result. Do the other two cylinders; Let us know the outcome.