Blossoms/immature fruit on peppers (and toms and eggplants etc) will also drop if the temperature is too low. I think it's average temps that matter, so you have to consider both daytime and nighttime temperatures as well. Peppers love heat, and the temperatures you describe are not all that high. I think if you are patient you will find fruit starting to set and mature as the season goes on. I would consider this early in Spring quite early to be getting pepper crops, but I'm not sure where you're located

The flowers may dropping so quickly due to the change of environment (either more or less light) and the shock of transplant. The color looks fine. I doubt you have rot already, but...that soil looks too water retentive for cacti. You want to mix it 50/50 with perlite, pumice or small lava rock. I would also gently secure it to a stake or something else tall because it's likely to be top-heavy...maybe that's why it's tilting. Just a general suggestion for when you buy a new cactus or succulent: don't change a lot of things all at once. Bring it home, set in a spot with good light (dappled shade or morning sun only, not full sun), and let it acclimate for a week. Then if you need to repot it, repot it and let it sit dry for a day before watering, and once again acclimate it to more sun very slowly. Start with dappled shade for a week, then add two hours of sun per week. A tall plant like that might be top-heavy as well so you might have to (gently) secure it to a stake.

I am no expert because these plants don't do well in my climate. But I wonder if it is a pollination issue? If flowers aren't pollinated they will abort and drop off. A bit of Googling might help you find out if this could be the case with your Physalis.

Someone may have taken the flower for food. Banana flowers ... well the hearts mostly ... make a great salad. The dressing is similar to a Thai green papaya salad dressing. I think they can be used cooked as well. My neighbor has five flowering banana trees and is getting ready to cut two stalks of bananas and is going to give me the flowers to make salads with. Yummy. I hired a man to help me with yard work one time and he took it upon himself to trim all the lower limbs from my grapefruit tree so we could walk under it. He said it would be easier for me to mow now that the limbs weren't in the way. I was furious and told him not to cut one darn thing ever again. I like lower limbs for the ease of getting fruit and for privacy. It's insane what people will do if you don't supervise their every move. They do what they would want ... not what we (the folks who hired them) want!