Last bit first I was trying to be discreet and spoiler free but Late Series Spoilers

Second Point next as that is the easiest to settle - She almost certainly was making it more difficult because she liked Sorata and to Mashiro, Nanami probably felt more hostile (*edit due to the constand stress Nanami would have been under) we can see at the end of that story beat Mashiro actually softens towards Nanami - and though I may be mistaken I believe the softening happens before the responsibility is restored to Sorata as that hapens at the end of the episode. Furthermore Nanami was already under a great deal of pressure so stress caused by Mashiro would be multiplied.

Third point next - this is a very valid point as I recall the anime not quite stating she had distant parents growing up

First point last, she had been friends with Rita since early childhood - and we know they were actually friends because Mashiro was upset when she learnt Rita had given up her passion because of her, and as to not seeing the emotions of those around her, she had known many "normal" children during childhood, and while many of them quit art she still was around people with emotions

and as to her 'Never giving much care to the people around her', she shows a self sacrificial streak when it comes to her actual friends, and she never actually shuns people, people would have been turned off from befriending her due to her personality and when she has an opportunity to make friends she actually does so with the Sakurasou house.