What's the difference between tactical and strategic nukes? Tactical can be launched from many different delivery systems. I don't think it's being done at the moment, but technically a shoulder fired system like a javelin could carry a tactical nuke. The power of that is small enough to level a part of a town, or a small village, without too much pollution.
It would. It has been clearly stated that there would be conventional retaliation, but to a large effect.
The use of an strategic weapon against Ukraine would carry an extreme response but it may not be a nuclear response - the US can retaliate to an equivalent degree without nukes. A Ruzzian strategic nuke against a non-nuclear power might even be too much for China to keep supporting Ruzzia.
If you think of it an strategic nuclear attack by Ruzzia would convert all their second strike capability platforms (e.g. subs, bombers, ...) and all their primary strike capability in valid targets. My guess is that these would be attacked in first instance, but to a very large extent, to the point that the Ruzzian capabilities will be halved in days. I do not picture a nuke in St Petersbourgh, Kurst or a large civil target as a first response.
If any excessive radiation gets into a NATO country, it is an attack, and it is not that difficult even with a tactical warhead.