Hi Erik
I can't answer all your question but since I use until recently PSR-9000 pro, I have some ideas
3) The low C and D key no longer work. Can this be repaired?
Probably you have to change the "key contact rubber strip" which is located under the keyboard. Although on some Yamaha models the split this strip to pieces, PSR-9000 has a "one long piece" strip. last time I change it cost me +/- 60 Euros
4) Is there a simple piece of software where I can convert the melody into notes?
This has nothing to do with PSR-9000. There are some application for computer to do what are you looking for but don't wait something very accurate. The only way I managed until now to get "descent" results was with perfectly quantized MIDI material and still you have to make many changes.
5) Because I have not a Diskdrive on my iMac, is there a possibility to load Styles in another way then via Disk?
I think it's time to invest 50-70 euro for a decent USB floppy emulator for your PSR-9000, then you can use a simple USB stick instead of floppies.