I do not know the exact dates. However, it is my understanding that the Mini arrived here in its second year, 1960. I believe it was the stronger safety regulations of the late 1960s that stopped importation. I think this occurred around 1968, shortly after the introduction of the Mk2.
The U.S. rules state that a car must be at least 25 years old to be imported. The 1991 you are interested in meets that requirement. There are a number of people who have imported the Japanese cars to the U.S. so they could have a Mini with air conditioning. However, what you have to keep in mind is these later cars were fuel injected instead of carbureted. That's great if there are no problems. However, very few people in the U.S. can service the injection system if problems develop. The later cars also had immobilizers as anti-theft devices. I remember several threads over the years where weeks were spent trying to troubleshoot why a late model Mini would not start.
They are nice cars and I'm sure you will enjoy it. Just remember that late model cars are unique over here so getting support and help can be more difficult.
Your second question concerned when they were sold here again. The Mini was never sold here by dealers after the late 1960s. The new car is not a Mini (capital M, lower case ini). The new car is a MINI (all capital letters). BMW bought Rover (who was making the late model Minis) and encouraged the development of a modern replacement for the Mini. The first of these new MINI cars was introduced in about 2001 with importation to the U.S. starting almost immediately. The capitalization distinction of Mini and MINI was implemented by BMW who strongly defends both as copyrighted. BMW has used several of the old Mini model variant names for the new MINI. Frankly, they have misused them but they have that right since they own the trademark.
The Mini Clubman (old car) was a re-styled Mini where the rounded lines of the Mini front end were squared off to make the car look "new" for the 1970s. The new MINI Clubman was the name BMW gave to the MINI wagon. This was a discontinuity with the old. The old Mini version of the wagon was the "Countryman" and/or "Estate" (I forget what distinguishes one from the other). Instead, BMW used the Countryman name for their supersized, not-so-mini available with four wheel drive. I would have preferred they used the Countryman and Clubman names more like BMC had used them in the 1960s. I have a friend with a MINI Clubman. He really likes the car but is very unhappy with the cost of parts and service.