I feel for you!
I used to work night shift and have to try and sleep in the daytime, but it was next to impossible to do during the summer because there was construction, trucks, boats on the river, etc. And the noise sometimes started around 6am or earlier if there were garbage trucks picking up the garbage.
Back when I was in nursing school I moved to a smaller, less expensive apartment near to the school so I could save on travel time and transportation costs. I lived on the main floor, which was kind of like being on the second floor because the basement was "above ground", and the only windows I had were in my living room (I had a bachelor apartment). There was a larger building next door that completely obliterated the light from getting into my apartment and it was pertpetually dark! I had to have my lights on regardless of the time of day, even in the summer. I absolutely hated that!
The space between my building and the other one also caused a tunnel effect for the wind, and the wind passed directly by my windows and I never got even a whisper of breeze. That made my apartment always feel damp and musty because there didn't seem to be any air exchange.
I was constantly sick with respiratory illnesses while living there. So sick one time that I ended up in the ER and missing 5 weeks of school.
And then there was the noise from their building!!
I lived there for 2 1/2 years. Once I finished school and got a job, I moved out! By that time I had developed asthma and a number of allergies to a variety of things. Things I didn't have when I first moved there. I truly believe that the building itself was sick.
So far as the shaking of your building is concerned, that causes structural damage to it. You should contact the owner and let him know how bad it is and that it has to be causing some problems with the foundation IE: cracks, sinking etc.
IMHO if that building is going to be so close to yours that it blocks out sun and air, I really think you should consider moving.
The building I'm living in now faces a river and the nearest building to my windows is way across the river. It's why I moved here and part of the reason I am loathe to move.