approach lights
 

Yes you can, as long as you have a serviceable ILS it does not matter what lights you have working or not working.

Surely, that should be a Day Cat1 app only? CatII/III "should" be ok without safeguarding.
At night......see the ryr/stn thread
watp,iktch

You can clear an a/c for an ILS for one rwy and land on another ie. circling app, not CATII/III but still at night.

Certainly in the UK you can clear the aircraft for an approach - as long as you have told it that the lights are u/s. Because it's a pretty major unserviceability in some circumstances I would probably tell the pilot about the lights and then ask his/her intentions - if the pilot says "I'd like to make an approach", then I'd clear it for the ILS or whatever other approach it wants.

ILS
 

Yes the approach lights are a part of the system, when not working the approach plate minimums will take this into consideration by changinging the Decision Altitude, also consider that on a CATIII approach, approach lights do not come into play, they are behind you at DA.