Any instructor in Jiu Jitsu will have the skills to be able to fall and land safely. I remember Helio slipped over in the bathroom when he was 94 years old. The doctors all asked him how he didnt injure himself because many older people get injured even by a stumble. He simply replied that a life time of falling and landing correctly means he will never be injured in a fall.

There is a correct way to fall and a very incorrect way to fall. Anyone with quality training in a grappling art will know how to fall and land correctly so not to hurt themselves, especially just for training purposes which your instructor would be doing. So NO Jiu jitsu would not be the reason.

As for your other question of can brain injuries occur from throws, the answer is most definitely YES, a good throw will easily kill a person who is not trained to land correctly. A throw can be a devastating act that is very seriously under appreciated. In fact during the time of the samurai there were throws regularly used that would see the opponent thrown onto the head to break the neck, clearly today these are rarely trained simply because we would run out of training partners lol.

Possibly, but mostly only if you don't land correctly. In Judo, for instance, the first thing you're taught is how to land safely when you're thrown. Among other things, you tuck your chin so that you don't smash your head into the mat.

PS-diagnosed with borderline what?

Can you get any permanent damage or develop some kind of condition of martial arts that contain throws/sweeps etc.?

An instructor of a jiu-Jitsu class in my area has been diagnosed with borderline so that's why i'm starting to wonder if it could be from that.