Is it fine to send a message to the author of a paper if I don't understand something and want to clarify it?
By all means ask. A person who goes through the trouble of writing up lecture notes, is almost certainly a person who would be happy to answer.

As someone who receives a lot of questions from PhD students myself, here are a couple of pointers for how to phrase your question. This could be obvious to you, but I know for sure that it is not obvious for everybody.


If you have a local supervisor, it makes sense to ask them first - maybe it is a trivial question.
Read the paper first, and use the notation from that paper when you can. 
Cut to the chase as quickly as possible. Don't explain their paper back to them in the mail, they know what they wrote.