Are women receptive to being cold approached in stores, grocery stores, etc?
No. Please don't do this, man. Some creepy dude (nothing to do with his appearance, everything to do with his body language) cold approached me in the market last week while my fiancée was an isle over, and he got himself doubly humiliated when he refused to admit it was a simple mistake. It was a cringeworthy experience for all involved.
Go join a club or attend some social activity - I'm talking festivals, concerts, galas. You're not going to be well received if you're interrupting someone on a singular mission like buying cereal lol

. If you're a professional, join professional orgs. You can join Black orgs too. shyt I met my fiancée through a black professional org. Orgs and clubs establish that you've got something in common.
You're anxious because you're not used to interacting with women as people. Which we are

. You're at an age where women your age are actively seeking long-term relationships, so you're in luck in terms of finding long-term companionship when you're ready. You should go and explore your options though. However, go interact with women without the aim being getting your dikk wet. You need to see it as a possible side effect of your interaction. Once you interact with them as people and don't let their womanhood distract you, you'll start making connections. Trust me when I say that lots of women are willing to overlook social awkwardness and such when they like you for who you are.
Also, go get in shape. You'll feel a lot better about yourself when you're taking care of your body.