If I boil potato in water (with skin on), is it safe for me to refrigerate it and eat it the day after...Also, is it better for me to peel it before refrigerating it or is it crucial to put it in bag with less possible air in it. Thank you!

Always take food safety precautions seriously and use refrigerated, leftover prepared potatoes within two days. This applies whether potatoes are peeled or how stored – although airtight containers will help prevent potatoes from dehydrating.