If my opponent is already affected by a special condition, let's say poison for example, and he then places Unown G on his pokemon, does it remove the condition? Same goes for any effects already on the defeding pokemon?
no it doesn't. unown g only prevents the effects of attacks to the pokemon he is attached to after he goes on. so if you are already poisoned it remains until you either bench it or evolve it. the same goes for any other condition and things such as smokescreen attacks.
Its all in the wording. If it says:
"Prevent blablabla....", then its indeed not healing.
Had it said "cannot be affected blablabla", THEN it would heal.