I was turned away at the border almost 6 or 7 years ago as I was travelling with someone who was suspected of trying to enter for the purposes of working illegally in the states. Niether of us was given any paperwork, but our identification was noted and we were returned to Canada. I have not had reason to visit the US since then. Is there a way I can find out if I am now considered "unwelcome", or am I worried for nothing?

From what you told me, you were not formally "excluded" from the United States. They simply refused you entry. As a result of this, however, your name was probably put into the "visa lookout" system. This means that a red flag is supposed to go up when you try to cross the border. Nevertheless, a considerable period of time has elapsed since they turned you away. It is entirely possible that you are no longer in the system. Even if you are, all this means is that you will have a harder time overcoming the presumption of immigrant intent. You can still overcome the presumption by documenting the purpose of your trip, providing a letter from your employer showing you have a job in Canada, providing a travel itinerary of where you will be while in the U.S., etc..

If you want to confirm that you don't have a problem before spending money booking your vacation, you might try taking a short weekend trip to Buffalo, NY as a test. However, this may not be a complete answer since they do not always enter you into their computer. Alternatively, you might try talking to an INS officer at Toronto International Airport. He or she might be willing to check their computer for you. However, you risk drawing attention to your previous encounter with them.

How can a University of British Columbia medical school graduate, who is now doing a medical residency training in the U.S., obtain a permanent residency status? Can he get a H1 visa, enabling him later to get permanent residency status? or can he go straight to permanent status, from his student F status?

Your question is not entirely clear since if you were doing post-graduate medical training in the U.S., you would not be under F status. I assume that you are asking which visa is used for post-graduate medical training. Such training is usually done under either H-1B or J-1 status. J-1 is more commonly used but J-1 visa holders are subject to a two-year foreign residence requirement after such status ends. You cannot do your post graduate medical training under an F student visa since clinical patient care is part of your training. If you want to be petitioned for permanent residence while doing post-graduate medical training, you must be in H-1B status since the doctrine of dual intent is not recognized for J-1 or F-1 categories.