WOW! That's the brother to mine! The color should be Garnet Brown, though, not Briar Brown. It was made by spraying green over red: I discovered that when my tank bag wore thru the green layer, decades ago.
For the oil: pull the sparkplugs and hook up a battery charger (nothing bigger than 10 amps, though) and use the electric start, 5-7 seconds at a time, to bring the oil up. Much easier, works better. Then change the oil and filter: it will stay primed but you will have to spin it a little more again to fill up the empty oil filter then. It will hold 4 quarts, showing about 1/4" high on the dipstick afterward. That won't bother anything: mine has been that way forever.
The spark advancer will be the AD125 Hitachi unit, most likely. Someday, think about cutting 1/2 turn off one of the springs to increase the low-end torque about 10%-15% and also reduce sparkplug fouling, by increasing the low-speed efficiency a little more (and use regular grade gas in town, midgrade for freeway, premium only if touring interstate speeds continuously). When you take the carbs apart, all they should need is a good cleaning and maybe new float bowl gaskets: soak the float valves clean for a couple of days in lacquer thinner, and keep the float valve with the same seat.
The swingarm bushings might be zamac plastic (like mine were) as this appeared until about 2/1972 production on the K2. If so, the edges of it may chip when you wrestle the swingarm collar out. If that happens, I can help out with a swingarm rebuild that will probably outlast you and the bike.
Ah, the K2: zenith of the 750K design, IMHO. Write with any questions, would love to answer back! Send a picture of the tank and side covers, too. Mine are in such nasty condition....the K2 seat foam is unique, having a bead on the seat cover that dipped down along where your thigh presses against it when you are standing still. The cover is still available: I have a genuine K2 foam and cover, don't know if I will ever use it, if you go the stock route. The K0-K2 had the legendary seat foam with the punched-out cores under your tailbones to make the famous "superseat in disguise" as Cycle Magazine called it in 1971. I did many back-to-back-to-back-to-back 1000 mile days on mine before I wore the original one out (in 1984).