My skin dries out in Ramadan from dehydration. Is there something I should do, change my moisturiser perhaps?

Adequate water intake and moisturising with hyaluronic acid serum will fix this problem for sure.

Best face wash for summers for acne-prone skin?

Acnes creamy face wash.

I use a pumice stone for my heels. Is that okay or should I limit the use?

No, it is absolutely fine to use a pumice stone for heels.

Since everything is closed, suggest the best way to

give myself a cleansing at home?

Gently exfoliate your face once a week. Also, opt for a milk-based cleanser to cleanse your face and wash your face properly twice a day with a good face wash. A proper skin care regime should be followed even at home.

I have excessively oily skin, how do I manage it in this weather?

Properly cleanse, tone and moisturise with a water-based moisturiser.