Yes, they are. They are free in all the countries of the UK. They're funded by money from the National Lottery.

Yes, they are. However, if they're hosting a temporary exhibition and you want to see it, they may charge a fee. - https://www.museumsassociation.org/about/faqs/# Also, the UK is made up of 4 countries (England, Scotland, Northern Ireland and Wales) so referring to the UK as England is offensive to those who live in Scotland, NI and Wales and will likely result in you being corrected or given a history lesson about the UK 😉.