Is This Normal - Running Competition

I assumed until the 3rd paragraph of your post that the problem was that 800m is really more of a middle distance and she sees herself as a long distance runner! Reading the rest I suppose that's not the case though...
But sorry, 800m is not a lot for a fit and healthy child. As others have said, my child started running junior park run (2k) at 4y/o. We didn't do any build up, just went for it. Obviously stopped and walked when necessary, but they managed it fine.
I would say that you're proud of your daughter for signing up for the race, that it will be fun and send her off to do it.

Bloody hell - I was the most unsporty of people at school (1980s), and certainly running was not my thing, and I had asthma. But the warm-up for every PE lesson was once round the 400m track. If you were in the last few to get round, you had to do it again!
Do kids really not exercise at all these days?

Loads of children a lot younger will have been doing Junior Parkrun (2km) for several years, even full Parkrun, so they probably felt there would be understanding what "long distance" was. I kniw my children were expected to run a lot longer than that in (State) Primary school PE.

800m is not far. It will be 2 laps of the running track. But I would take her out to practice a couple of times. It is useful to understand how fast you should go at the beginning. (Ie don’t sprint like your life depends on it but a decent run is fine!)

I would measure somewhere 400m away and run there and back as that will help her with the two laps thing.

Yes, it’s normal.

secondaries have lots of sports teams not all if which are for sports they’ll do in PE.

Normally they ask for people to sign up for the teams and for training sessions - the training sessions are often outside of normal school time and in a lunchtime or after school - eg football training, netball training etc.

but for some stuff they’ll open it up to everyone.

they are assuming that the people who sign up want to do it and are capable of doing it.

usually it’s students who do that sport outside school and want to have a go.

does your child do any sport outside school?

I remember PE in secondary school was always a trial by fire. Training to run further and faster wasn't really a thing, it was just something we were all expected to have a go at. None of it was optional, not even the long cross country runs.

I don't think 800m is an especially worrying distance to just have a crack at, most fit young people would manage it without any preparation.

if this is a state school then PE lessons are short. Most sporty children do sport either in after school clubs at school or in external clubs (or both). Is there a school athletics club?

I would also suggest you tell your daughter not to sign up for things if she doesn't know what they are, in the future.

2bh that only really three minutes running. Maybe three and a half. My 7yo did that on sports day and didn't train as far as I'm aware. Kids are usually fitter than adults unless she has a health condition she should be fine.