Schengen visa applications - domestic flight tickets, invitation letter, future trip plans

I am going to attend an academic conference in A Coruña, Spain. So I am going to apply for a cultural visa. I also want to spend a few days in Madrid just as a tourist.

1) I can make a free roundtrip flight reservation to Madrid which is valid for 10 days (I hope 10 days will be enough). However, I cannot make reservations from Madrid to A Coruña without buying the train/flight/bus ticket. I can make hotel reservations for both Madrid and A Coruna on several websites for free, as you know. Visa application center representative on the phone told me that I need to submit domestic transfer reservations as well, but it isn't explained in the required documents list, so I am not sure if she was confident or just trying to be safe. So, should I buy the tickets from Madrid to A Coruña and back? It will cost something around 200 Euros, but it is not ignorable when you convert it to my local currency.

2) The conference organizers sent me an invitation letter by email, and they resisted to post a physical copy signed with wet ink at first, but I insisted and they have sent. However, it didn't reach, and probably it is lost in somewhere, so I only have the softcopy. This conference is a relatively reputable and big organization, and the program of the event can be reached from its website which includes my name, and presentation date and time. Would it be enough this way, or should I apply for a tourist visa instead of cultural and not mention the conference at all?

3) Although I don't have any plans to visit another country this time, I would like to get a longer visa with multiple entrance in order to do short weekend visits to Europe in the following months. Is it okay if I select multiple entrance in the application form this time, and maybe mention it in the letter of intent?