[my name] you can always speak to me and I don't know of anyone who hates you you're such a lovely person. If someone says this to you, would you think that they were your friend/cared about you?
They sound patronising to me like they are doing you a good turn in offering your friendship.
It depends on the context, and how they act in general.
If I thought they were being sincere, I'd probably say yes.
NAS24919 I would side with Raindrops on roses on this one. To me, this person sounds as if they are trying a little bit too hard- almost like a false friend that would give you some sort of false assurance... However, as Cloudy Mountains has said below, it does depend largely on the context... Could it be for instance, that this person in question was just trying to console you but just didn't know what the best thing to say would be?
Yes, that sounds really supportive to me and as though they care.
I'd be careful of pulling away from people because their behaviour is deemed as 'fake' by some. Before I knew I was an autistic individual there were many times in my life where I followed a social script as I wanted to say the right thing. Although it wasn't natural and may come across as fake good intentions were there.
They might be a people pleaser so said this to get in your good books. It depends on the context.