You are so going to love driving an EV, I made the switch two years ago and have never ever regretted it. I have a charger at home and do 90% of my charging overnight using cheap rate electricity, so I'm definitely not an expert on public chargers, but I'll have a go at answering your questions.
a) if you're a member of, say BP Pulse, can you only use their charging stations? Or can you use the others if you pay? - you can use any charger if you pay, most now have contactless payment as an option so you don't need to have a subscription, however if you regularly use a particular charger it can be cheaper to take out a subscription.
b) if there's a charging point in for example a pub car park, is it ok to use if you're not using the pub? Yes absolutely, not necessarily the same with hotels as sometimes the chargers are for guests.
c) if it's a pay car park I presume you still need to pay and pay for your electricity? That depends on the car park, some councils offer free parking for EVs regardless if they are charging or not, some expect you pay to park and pay for charging. Check the rules on the signs every car park is different. Some supermarkets offer free charging and free parking.
d) is there a time limit on how long you leave your car there? There's a lot of discussion about this, there are no rules but some consider it bad form to leave your car charging for the last 10-20% as this is when the charge slows down. You would be very unpopular if you left your car on the charger after it had reached 100%, they aren't meant to be used as parking spaces.
Is there anything else I need to know?* It's cheapest to charge at home so if you can get a charger installed. I pay 5p a unit for night time electric, my EV costs be under £10 per month to charge. If you are regular user of public chargers you will pay a lot more.
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Download some apps of where chargers are situated, Zap-Map and WattsUp are good and really help with planning longer journeys.
Final piece of advice is just enjoy the feeling of electric driving you'll never want to drive and ICE again.