Learn English – How to address people at the beginning of a conversation

So, the preferred method of addressing a professor in the US is not entirely consistent. Variations from university to university or even department to department occur, however, at the three universities/departments I've attended/been employed by, the following is true:

• If the professor holds a doctorate, calling him/her Dr. Lastname is the most common in my personal experience, but Professor Lastname is also very common, especially in departments that have faculty with a lower percentage of doctorates (since with Professor you don't have to know whether they hold a doctorate)
• If the professor does not hold a doctorate, Professor Lastname or Mr./Ms. Lastname are common
• In the US, the difference between professors and lecturers is not as clearcut as in other countries, especially to students. In many cases, they may not actually know whether their instructor is one or the other and so, in general, the same rules apply as to professors. As an example, when I worked as a visiting lecturer, I was referred to frequently as Professor, even though that wasn't my actual title.

A few other notes

• The length of the last name of the professor doesn't really change things. If it's hard to pronounce or spell, you may wish to avoid it by simply saying 'Professor', but it doesn't entitle you to switch to the first name or some nickname.
• Some instructors may prefer being addressed by either their nickname or first name. However, you should only do this after being explictly told to. I've had professors who preferred Professor Firstname or just Firstname, and they'll usually say so on the first day. However, I've also had professors get offended when students referred to them using a more informal form of address.
• Using Prof. as an abbreviation of Professor is fine if you're merging it with their name, just like Dr. is for Doctor.

"I wouldn't have bought any cheese" is expressed as a deduction (as in the discussion you follow up with) "it's not likely I bought cheese", or "I'm not the sort of person to have bought cheese there".

The pragmatic implication in this sense is either "I don't remember for sure whether I ever bought cheese, but I can't believe I did", or possibly "You must see that I'm not the sort of person to buy cheese there".