Possible daft Brexit question...?

[AuchAyeTheNo]

I’ll be honest. I have absolutely no clue what is going on with regards to brexit.

My question is though. Regardless of the date we ‘leave’ if I was in a EU country that day would I be expecting anything to happen immediately? I’ve got some trips booked till the end of May and I’m slightly worried about travelling home etc.

Get all your Euros now, because No Deal will send the £ through the floor.

It depends on if there is a deal or not.
Assuming no deal:
Six months at least on passports
Green card for car insurance
International driving permit
Private health insurance (no ehic card)
Much more complicated to travel with your pet.
Much longer queues at airport/ ferry

I have Euros and at least a year left on my passport plus company health insurance. Every time I go I will be flying so I guess I’m just worried over something silly like immediately stopping flights back to the UK.

Can I check if your passport is more than 10 years old? If so, regardless of time left on it, please get it renewed.

There are no plans to 'stop' flights BUT in a 'no deal' scenario the EU will be certifying planes etc and they have said that UK owned/operated airlines will not be permitted to do 'round robin' flights, only point to point. So London/Paris/Berlin/London would not be permitted for example.
This would mean a bit of rescheduling which will be a PITA but workable.
The EU have said this can continue up to either 9 or 12 months (forgetting details) and can be withdrawn at any moment the EU sees fit. This probably sounds more scary than it would appear but unless the UK does something really silly (!!!) they would give sensible notice period as they don't want planes 'stuck' in awkward places.

What happens if you are travelling in an EU country on a UK passport (so didn't need a visa) on 'Brexit day' and it is No Deal? Would your visa-free permission to be in that EU country finish abruptly? Could you apply for a travel visa whilst staying in the country?