I know someone who was fined for travelling to a lower tier area to go to the pub. Police boarded the train between the cities and issued several penalties. Fines to individuals for this sort of offence will be at the minimum level.
The £10k fines will be for organising gatherings, eg weddings, raves. I've read about a few of these being issued locally.
Travelling outside your area for a walk - I think this would depend on risk - it's a 'should' stay locally not must. So if you drive to a quiet area to the other side of your own city, that's probably fine. Drive an hour to a crowded beauty spot along with thousands of others and park your car on a narrow road because the car park is full, probably not.
Travelling to see a friend indoors - again, this would depend. If the friend is vulnerable due to shielding, mental health issues, potential domestic abuse etc, that's probably legal. Socialising, not. Again, someone I know says she knows several people who've been fined for visiting friends and relatives when checks were made in an area where compliance has been poor.
Travelling to meet a friend outside - this is legal, but would depend how far and where you meet - see above. I'd say unlikely to be fined for this unless clearly outside the spirit of the guidelines.
Shopping more than once a day - There are no rules about where you can shop or how often. No-one is going to be fined for shopping multiple times a day or going to multiple shops. You are encouraged to go 'as little as possible' and 'stay local' but you're not required to do without things that are not available, or only shop in your nearest shop, and if a shop is open, you're allowed to buy anything that it sells, you're not required to only buy gruel.