My daughter is also 8yrs old, an only child, and going into third grade next year with a new teacher after having the same teacher for 2 years. She is very shy and does not do well with change. This past weekend she slept over a friends house for the first time and did better than we expected. (She took a favorite stuffed animal and a book with her.) She was never willing to go to sleepovers in the past so we would have her friends sleepover at our house. This way she did not feel that she was left out of anything. You might want to try to have one of your daughters friends sleepover your house. Your daughter will get an idea of what sleepovers are like and might be more willing to try it at someone elses house.
It's such a shame that life doesn't come with an owners manual. When I encountered issues such as this with my kids (my daughter had separation anxiety), I decided to approach the problem by first figuring out how *I* handle new situations and then showing or explaining that to her.
Often new situations bring with them a range of expectations--not only does one need to know what to expect, but one needs to know what is expected of them. That can be complicated and anxiety producing, so it's always good to have a plan when dealing with new things.
So, maybe if you not only encouraged your daughter, but gave her some guidance on *how* to do new things and what to expect it would help. Also discussing the "what if" situations...like what if (at an overnight) she wakes up and finds out she isn't in her own room and gets frightened...maybe she could pretend to be in her room, or snuggle her stuffed animal she brought with her, or think of her favorite story until she falls back asleep, or... you get the idea.
If it's other new situation, maybe she just needs to know (ahead of time) what it is she's supposed to do. Like how *do* you buy a movie ticket? It's like wanting or needing to know the "rules" ahead of time.
As far as the school situation, I would look for books and movies that have characters in similar situations, watch and read them with her and come up (with her) with a plan for how she is going to handle it.
Sometimes all one needs is a little success at a new thing to gain confidence at it.
Your daughter's separation anxiety is a problem because it keeps her from participating in situations and activities that are the norm for her age. It is wise not to pressure her, but it is also wise to introduce her to situations in a calm, patient, supportive way in order to counter her avoidance. Si it's sort of a balancing act. Should you defer all the time to her worries? No. Should you exert undue pressure on her? No. Should you try to help her acclimate to situations by supporting her involvement? Yes. It would be wise to arrange an evaluation with a child psychologist (or other child mental health clinician) who can assist you and your daughter to manage the anxiety.