Using wrong speed/size cassette on trainer I have a 10-speed bike and my wife an 11-speed. I have burnt enough old tyres on my indoor trainer so decided to try a trainer specific tyre on an old wheel.

The old wheel currently has an 8-speed cassette on it. What would be the effect of using that with my bike and my wife's bike? I'm guessing this would be pretty horrible.

What if I change the wheel to a 10 speed cassette (which is what I will probably do) will my wife's bike work?

My current rear cassette is 11-23 if I put a bigger cassette on say 11-28 I expect my chain would normally need to be lengthened. If I don't lengthen my chain will I just lose the use of the largest cogs or would there be worse consequences?

I have no concerns about poor shifting or missing gears because it's only on the trainer. As long as I can get in one gear that's enough, the trainer has its own difficulty adjuster. Wear on the chain or damage to other parts would be a concern.
As you suspect, you cannot use the 8 speed cassette with either bike. The indexing will be completely wrong.

8, 9 and 10 speed cassettes use the same freehub body so you can put a 10 speed cassette on the wheel. The sprocket spacing on the 11 speed cassette is different from the 10 speed, so that isn't going to work, at least not very well. Maybe you could get a few gears to work.

If your derailleur capacity and chain length don't allow the use of a 11-28 cassette, you will be OK as long as you stay off the sprockets that are too large. If you can't use a 11-28 cassette, why fit one? I guess you happen to have a spare lying around?