Can a R/T flight be split between the two programs with each leg credited to one of the programs?

yes, but either change the frequent flier number just before that next leg (this will change all following segments, but not tha one you did already fly), or don't enter a frequent flier number at all (if you are not waitlisted for any upgrades) and send in the documentations to the programs afterwards.

Can the two legs of a 1-stop flight (with different flight numbers) be credited to separate programs? - yes, same as above (you can change the ff-program even with your boarding pass for the second leg already in hand).

Do we know for sure if LH is treating Austrian and Tyrolean as two airlines?
It is not LH, it is miles&more (OS being a miles&more-member), that will treat all three OS-Group-airlines as one for this promotion. And, nothing these days is for sure ;, but we FlyerTalkers seem to know the rules better than the programs themselves ...

If so, does it mean that Austrian (OS) ticketing on Tyrolean airlines metal (which is the only way to fly Tyrolean) not eligible as a code share or is it counted as a leg in Tyrolean?
See answer above, will be 'treated' by miles&more as a (valid for this promotion) OS-flight.