That is a very nice, tidy looking bike you have there.
The “red” coils if it is a single plastic encapsulated double ended coil, is probably a Dyna coil – if so this is a good thing. OTOH, if you have two separate red coloured cylindrical coils, they could be any bloody thing, which isn’t a problem providing the resistance is correct for the ignition trigger.
Your bike probably left the factory with a Bosch hall effect triggering system (combined with mechanical advance retard), before giving advice on the “correctness” of the coils, we need to know how they are triggered, i.e. points, stock hall effect, Boyer Bransden and numerous other after-market triggering options are out there.
The charge light being on at idle is both normal and a “design feature”. If your red light does not come on at idle, chances are that the bulb has failed (which interestingly means no charging BTW) or that something dire has happened. The good news is that the charging system, whilst a little weak kneed at only 280 watts on the best day it ever had, is just about as reliable as a ball pein hammer.
Squealing brakes is unusual and worse may be the result of a number of causes. If the brakes feel like they are working OK, I’d be inclined to throw a new set of pads into them and see if that makes the noise go away. If it does not, then there is an investigation process to follow.
Like everything else on a BMW the final drive and transmission are designed to give long and relatively trouble free lives, but do bear in mind it is now a 30+ years old motorcycle. The big thing with final drives is wear on the drive splines, usually the result of inadequate or incorrect lubrication, there is polite conjecture here at the moment as to the best method and cost of fixing drive splines, the only real consensus is that it is not cheap. Seals wear out but are replaceable by an adventurous owner.
Gearboxes that have not been abused and which have not had water sneak past an old or improperly fitted speedo cable boot tend to last a long, long time – the more so as it is the same gearbox fitted to the R65 as was fitted to far more powerful siblings. The only known issue is with the spring that provides the detent “feel”, this is a known failure item and is unfortunately a labour intensive fix as removing the gearbox involves first removing the rear sub-frame and swing-arm. Replacing the gearbox bearings etc is not a job usually tackled by the home mechanic as it requires special tools and precision measuring instruments (along with the practiced skills to use them). That said, in the Facebook airheads forum a Norwegian fellow has just done his own gearbox up successfully (they have a long winter) using material gleaned from the web and the input of more experienced group members.
Fork seals are easily replaced, in fact after the experience of some of the Japanese bikes in your stable, they will be a breeze. At the risk of admitting something I am a little embarrassed over, if you decide to remove your damper rods – you take them out via the bottom of the forks – well you can take them out via the top but you will never put them back in with all piston rings intact from the top.
Things to look out for.
Check for any knocks, grinds etc in the crank or bottom end – problems here are bluntly a sure sign of abuse as given clean oil and not being thrashed the 247 bottom end should do at least 500,000km.
Valve gear noises should be investigated – mostly this will be ham handedness on the part of the owner, but there are some dire things that can happen.
Our beloved R65s for some reason are a little prone to dropping valves, my own view (not shared by some in this group) is to change exhaust valves at or before 50,000km (32,000miles). There are also some who suffer valve seat recession said to be the result of unleaded fuel. The thing is, not everybody has valve seat problems so I would definitely NOT spend money on replacement seats until and unless I found that I did have a problem.
Oil leaks – these are usually easily curable - lipped seals at front and back of engine rarely give trouble, but cylinder bases will leak if they are allowed to “fret” due to failure to maintain cylinder head bolt tension. Pushrod seals will leak eventually, but they usually last long enough for you to be doing a top end refresh anyway.
Exhaust systems the chances are pretty small that you will have an original exhaust system still fitted, if you do, start saving for its inevitable replacement. The “gold” standard replacement exhaust system is stainless steel. The Australian made “Staintune” is the standout best as they are a copy of the original equipment externally, with small modifications to make them more free flowing without becoming loud. Next best is the English Kehin (spelling?) and after that who knows.
Shock absorbers – the original Boges should be placed in a box for posterity and replaced – I like Ikon (the now Australian owned Koni shock absorbers)