I think she does realize she has people in her life. The only times we see her not appreciating them is s7, the season of "wtf is going on?", as I like to call it lol.I agree with most of this and I don't hate Buffy the character, but it does make me like her character less because we spend 7 seasons watching her with people who love her, obviously she goes through a lot of pain but I wanted her to recognise that she had people who could help make the pain go away if she let them.
On the Faith blaming Buffy thing, I did cringe when she did that, it was absolutely the worst thing that she could have done but I think she did it because she felt like nobody was going to have her back and that she was going to be sent to prison. In short I think it was out of fear.
You can say she didn't appreciate them in s6, but I think that's a major stretch. Her friends resurrected her, left her to crawl her way out of her coffin, and then were so consumed with their own problems it's like they could almost care less that she was back. I know they didn't know that they pulled her out of heaven, but none of them ever really tried to see how she was feeling once back on earth regardless of what dimension they pulled her out of.
Otherwise, I'd day Buffy was pretty appreciative of her friends and family.
Yeah, I can definitely see that fear was Faith's motive. I just don't know how she thought this was going to go in her favor because of course Giles is going to trust Buffy over Faith. She definitely went with her gut reaction and did not think this through logically even a little bit!