Can nexus one phone or any similar android phone work, when its microSD is pulled out from it, and if only internal memory remained.
Yeah definitely it works fine without any issue. But if you have installed any apps on SD Card then they won't work at all. But to take backup of any data(Contacts, Messages, Call log) on your phone you should have SD card inserted.
Finally to answer your question, yes. it works fine as the OS and related information stored on the phone internal memory.
I own an HTC Desire and an HTC Wildfire, they both works without microSD. Apps stored on the card just becomes unavailable.
Yeah of course it will. But barely you can use it as a phone. You cannot even transfer anything via bluetooth(I have tried this with HTC Desire HD).