Since emails are a relatively new form of communication, there are no tried and tested formulae for how they should be written, as there are for business letters, for example. In fact, I think it’s fair to say that there is no correct naming format for emails, but that they tend to be informal. A quick glance through the emails in my inbox reveals the following range of greetings:

Dear Ms Potter
Dear Liz
Hello Liz
Hi Liz
Hello there
Hi there
Hi
Liz
Dear All
All
[No greeting]

An initial contact from someone who had never met me but knew my name began Dear Ms Potter, but by the second email this had changed to Dear Liz and then Hi Liz, so even when formality is used, it quickly gives way to informality.

I think it’s fair to say that if you know the name of a person but have never met them, then you can use their surname and title in the first email you send them (using Mr for men, Ms for women, since it is unlikely you will know their marital status; or another title such as Dr if appropriate). However, it is equally acceptable to use their first name if you know it: I wouldn’t object to being addressed as Dear Liz by someone who didn’t know me. If you don’t know the gender of the recipient I would suggest that a plain Hello is the safest option.

In subsequent emails, I would suggest that Hello or Hi plus the person’s name is a safe option; obviously if you know the person well you can use more familiar forms of address, up to and including no form of address at all.

As for ending the email, the most common sign-off, I think, is Best (short for Best Wishes) followed by your first name. I would only use my full name when writing to someone I didn’t know for the first time. You can also use formulae such as Regards, Yours, Best wishes or All the best (this last sounds quite cordial to me, so I use it when I want to sound friendly or appreciative).

As far as I’m aware there are no differences in usage between UK and US English.

Could you let me know which form you would choose – a, b, c or d - in the following situation?

You are watching television. Someone else comes in and changes
a. channel
b. the channel
c. channels
d. the channels.
You say: ‘Hey, don't do that, I'm watching!’

Traditional grammar says that ‘change trains / jobs’ is the only correct usage, but 'channel' seems to be an exception.

You could say: I was studying English, but I changed course and now I'm studying History; this is because you changed from one specific course to another. You might also say: Many students change courses / It is possible to change courses during the first month of term; here you are not specifying from which course to which course, so you use the more general plural (though you could also say: Is it possible to change course?).

I think that grammar books never cover all the possibilities, because there are just too many of them. At best, they give useful generalisations that you can follow.