What year is it? I see square MC, dual disc, clam shell air cleaner and flat top carbs.
The ATE calipers, flat top Bings, clamshell air cleaner and short duck tail mark this one as a 79~80 model.
To the OP - lovely bike and welcome. If unmolested your bike has the small valves and non-hardened valve seats which means it may be prone to valve seat recession. If so the fix will onl;y cost a few diolalrs more to upgrade to the larger valves and unleaded tolerant seats which will give you a "free" 5hp. Alternatively a set of later model heads which already have the bigger valves and unleaded seats might be an alternative (post 1985 heads are the "Gold" standard but you need to get the rocker gear specific to that model.
I don't know what your level of BMW knowledge is, but I not that you changed the oil filter. If you didn't check the canister depth and calculate the correct combination of shims/gasket, then perhaps you should do so as loss of oil pressure is bad.
Next, given the time this bike has been standing you will want to do a gearbox spline lube, while you are there you can check the clutch. You should know that the "heavy flywheel" version of the R65 uses a pressure plate and clutch plate unique to that model.
Unless someone has been there before you, your bike will have the now rare "points in a can" ignition trigger. Contrary to modern thinking I would not rush out and buy a Boyer ignition kit for it - as I get older I yearn for the simplicity and reliability of points.
On the subject of ignition, once you have the "hot idle" problem sorted (in my experience almost always sticking advance/retard due to either lubrication failure or stretched/broken advance retard springs) Its time to check the timing. If you have a blurred or double image of timing mark when using your timign strobe you are goign to be at a minimum replacing the timing chain, but given thhe age and potential miles of the bike, likely the chain, crankshaft sprocket and (possibly) the cam sprocket. If you need to change the crank sprocket yoou will need to hire/borrow soem specialist (not special) tools - it is a time consuming job, but well within the capabilities of a home mechanic.
Lastly, when the rocker coveres are off, see how much "rock" there is in the valve guides - your model is somewhat more prone to other BMWs to the dreaded dropped valve and around 50K miles is well into the territory when it is likely to happen. The guides can be replaced, or far more cheaply k-lined which in my experience is just as durable, and best of all, wwhen they do wear the k-lines can be wound out and new ones fitted.
I'll leave others to discuss the joys of the final drive, but I will say that evenn if youy have to do everything I've mentioned above, the cost will be returned to you in decades of trouble free riding.
