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I would provide more water for them, if they are in containers. As we move into hot weather, and they form the potatoes, they will need more water. Watering once a day would not be too much. In weather where temps are over 85 F, water twice a day.

Wireworms, grubs, tuber worms, corn borers and weevils are all bugs that can tunnel into the potato tubers. It may also be a root maggot problem. There are many species of root maggots so their color may vary from one to another. However, their taste for root crops, like potatoes, is the same. Here is an article that you may find helpful: https://www.gardeningknowhow.com/plant-problems/pests/root-eating-insects-identifying-vegetable-root-maggots-and-root-maggot-control.htm

I've never heard of a potato morphing from red skinned to white skinned. Sometimes it's difficult to tell red seed potatoes from the whites. The potato skin will remain the color it is as soon as it starts forming, it might get a little more intensely colored, but it won't change.

I can't be 100% sure without seeing the damage, but it sounds like the red veining is nematode damage. With the hollow hearts, I am going to guess that sometime during the last growing season, your potatoes went through a rough bit with not enough water. This would have stressed the plants and made them more susceptible to nematodes and caused the hollow heart condition. I would recommend taking a sample of the potatoes into your local extension office to confirm nematodes. Regardless, I would start with clean seed potatoes this year. Do not reuse the potatoes from last year as seed. Move the location of where you grow your potatoes. This will ensure that this year's crop is not affected by the issues of last year.

This article should help: https://www.gardeningknowhow.com/edible/vegetables/potato/how-and-when-to-harvest-potatoes.htm

Yes, you can remove these roots to refresh your soil for next season.