If a job ad says 60-80%

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and in the waffle at the end it says "Equality and compatibility are important concerns for XXXXX. Part-time work is encouraged at all levels."

Ideally, I would like to work 50% because of DC. Does that mean that my application would be automatically rejected if I state 50% on it.
Does it mean that 60% is their lowest part time consideration?

Hard to say really, the only way to know for sure would be to call and ask - there doesn't seem to be a huge difference between 50% and 60% but it's possible that's a big deal for them. Personally I'd apply anyway and negotiate later but then again I've seen people on here say that's a huge no-no so who knows. Would you def not consider doing 60% in the right job or is 50% your absolute max?

Yes, I would consider 60% in the right job if there was the flexibility to e.g. work 3 days a week during term time and 2 full days and 2 mornings during the school holidays.

I wouldn't state it on your application. Apply for the role as advertised. If you are offered it, then you can negotiate. If they are advertising it as 60-80%, that is already part-time, so in keeping with their statement. But honestly, there isn't a huge difference between 50 and 60%, so I can't imagine you couldn't find a middle ground. But it's not something I'd ever raise pre-offer.

It really depends on the job as it could mean anything.

Are there busy/quiet times of year to cover?

Would you be expected to fit in with existing peaks and troughs in staffing?

Will they actually adjust workload for lower contracted hours/pay or do they mean 'we'll let you be present for 3 days a week, but we'll still expect you to do 4 days worth of work'.

Thanks for the advice!

I would not say 50% at this point, go and see but to me it implies they want either 3 or 4 days but can be flexible so could might be 5 days school hours is possible or maybe could do some from home. Where I worked they would not go below 60% but it varies, generally ask but be flexible yourself. Ours had to have same hours all year. But each organisation will have own rules.