Q: option key stuck (not physically)

First, try resetting the PRAM and the SMC and see if it worked. Those resets will restore some settings to factory status

Try starting OS X into safe mode, holding the Shift key while your Mac is starting. Can you type now correctly? Also, could you start into safe mode?

In that case, it's a hardware problem. Take the Mac to an Apple Store or reseller to see what happens to your keyboard. Did you spill liquid in the computer in the past?

Sorry for not being able to fix your problem, but the fact that you couldn't start into safe mode indicates a hardware problem

To connect a Bluetooth keyboard, first you have to start up into OS X and set up the Bluetooth keyboard with your computer here.

Then, to use your Bluetooth keyboard during startup to start into OS X Recovery, hold Command and R keys after hearing the startup sound

You can reset the user password starting into OS X Recovery. See > http://discussions.apple.com/docs/DOC-4101

Does the Air have a USB port (I imagine it does but I don't have one to look at)? On my old Macbook Pro I can connect a USB keyboard and use it, even for logging in.

WanjaBerlin wrote:

 

I'll try to remove and clean the option keys...

Good luck, but it really sounds like the kind of damage that needs professional repair/replacement.