What’s the best way to reheat frozen boiled potatoes

Best thing to do is to keep them out of the light in an cool dark dry place. I usually put them in a hessian bag to try and keep the moisture away.

Don't store them in the fridge or anywhere that gets direct sunlight.

I used to cook plenty of purple sweet potatoes when I was living in africa:) Sounds like you maybe cooked them too long...

They can be extremely tasty, sweet with a "perfumy" hint if you are lucky. They are best boiled with the skin on like you did and peeled afterwards (as the taste is preserved better that way). As for cooking time it really depends on the size (which means the potatoes are likely done at different times) but you can always feel when they are done by pressing on the potato with a fork - it should give slightly/be soft. I think it usually took me about 30min but I didn't use a clock. It may shorten the cooking time slightly to make holes in the potatoes with a fork (this also adds to the "creaminess").

I guess they do sometimes get a softer, more "creamy" consistency than your usual potato when well done. However the taste is richer and in my opinion far superior to orange sweet potato. If you prefer a firmer potato, just let your potatoes stay on the firm side (in my experience, though, the taste is enhanced by letting them go soft). But boiled ones would anyways mainly be for puddings as it gets rather sweet.

For panfrying I would suggest avoiding boiling the sweet pots first. Simply peel/wedge them raw, fry them as chips until done and serve with a spicy/hot dip - yum.