How to tell if player is unable to move
 

I would like to know whether "player" is rooted and I could look for the appropriate debuff but there are so many of them that ave same effect. Is there an API function that could tell me?

If it's only for yourself, you can probably use C_LossOfControl.GetEventInfo

See here for reference.

You can look in FrameXML/LossOfControlFrame.lua for examples of how the C_LossOfControl system is meant to be used. However, not every debuff that causes a Loss Of Control event is caught by the C_LossOfControl system, so you'll still need either some database to catch those debuffs or else scan tooltips for "[Rr]ooted".

I think it is academic now, the reason I was interested is because my DH could not move due to a spider's "Vile Webbing" I think the debuff was...

Is there a way to acquire a loss of control debuff for testing purposes? Play with a Rogue and ask them to stun you or with a druid and ask them to root you perhaps?

Test this with a mob that has the ability. Just be careful not to kill them.
Testing it with another player only makes sense if you query several roots / stuns.