Everest base camp trek is world popular trekking route. Everest base camp can be reached in these different ways.
Flight to Lukla and trek to Everest base camp
Drive to Jiri or Deurali and Trek
Helicopter flight direct to Everest base camp
It is strange that the online application system asks your for a proof of relationship, if the person you are visiting is a friend and not a family member nor a spouse. Double check that you have selected the right relationship during the process. In should be this Question 4 on this part of the application:
Otherwise, as you mention, there should be an ...