Hi and welcome to the madhouse that is EuroKClub!
I only ever use BMW oil. The clutch is really fussy about this.
You say you don't have an owners handbook but also say you read the owners manual.
BMW call the Owners Handbook a Riders Manual and this includes the service stamp section. A new riders manual is available from dealers. I have a K12S riders manual in PDF format if you need one.
There is also the workshop manual called a RepROM which is available on DVD from dealers for around £100 or pirated copies are available online for around £20 which of course we don't advocate...
I would be very wary of any bike without a fully stamped up service section in the handbook, but especially a K and even more so a K12, so I really hope you have the Riders Manual with all the dealer stamps for regular services. I'm fussy like that.
If you bought the bike from a BMW dealer then it 'should' be fully up to date with all the recalls of which there were several which are potential engine and even rider killers - camchain tensioner and jump guard are in the first category, seized dog-bone links in the rear suspension are in the second category as is the fuel tank outlet cracks (but I can't remember if that applies to the K12). If you bought the bike from a non-BMW dealer then it is worth checking that all the recalls and upgrades have been done. There were full recalls but BMW only does full recalls when pushed legally except in Germany and the US, otherwise they call them campaigns which is a way of saying there is nothing really wrong but bring it in anyway. And we'll fix what isn't really wrong.
Depending on the year of your bike there may also be the dreaded low-speed fuelling issue. This was sort of fixed on early bikes with a new airbox and idle control valve kit.
As for getting the bike dyno'd, there is very little that can be done without either chipping or fitting a Power Commander. There are no adjustments on the throttle bodies for example. Chipping has been used to good effect by at least two members, although one now much prefers the PC route.
Good luck with the bike and we look forward to seeing some piccies. Who knows, it may even have belonged to one of us a previous life. Brian