All those things sound pretty normal to me. And 22 months is just getting the stage where she is wanting to be independent bt of course is a bit little, so she is trying with the things she can control.
You might want to to pick 1 thing at a time. I suggest the running off as its most dangerous so will incentivise you to follow through and therefore help her realise you will follow through in other situations too. Tell her buggy or walking and if she won't hold your hand or the buggy then it's the buggy. Be prepared for yelling, just put her in and walk fast round the park, not shops for your own peace and avoid staring.
Running off- tell her if she runs off then she is in the buggy. If she runs- then straight in til home. Just ignore the yelling.
Then pick The next thing, but be reasonable til her- let her make choices appropriate. She isn't alone in not wanting to wear a hat. Let her have a grown p chair and get her a booster you can take out and about and praise her behaviour in the grown up chair. Go to coffee shops and show her how to behave and work up to restaurants.
She is running your life a bit too much. Supermarkets - in the trolley and have a snack. After, as you know it's dull then she can go on the ride. Messes about, still trolley, but no ride. Go when it's quiet and expect yelling. Smile at passers by and dont let anyone interfere. Don't get cross, she is just growing up:)