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I'm sorry that you are having this problem. Animal pests are a difficult problem for any gardener. Groundhogs, aka woodchucks, actually can climb like squirrels, and they eat gardens hungrily, so they are still a possibility. Rabbits, mice, and ground squirrels are also possibilities. Enclosing plants in metal mesh cages can be very helpful, even if you just enclose a few feet near the ground, at least for some animals. Here are some articles that may help:

https://www.gardeningknowhow.com/plant-problems/pests/animals/keep-rabbits-out-of-gardens.htm
http://web.extension.illinois.edu/wildlife/directory_show.cfm?species=woodchuck

Absolutely! This is perfectly fine, and I do this quite often myself. They do taste much better cured, but there is no harm in eating them fresh. Here is an article for more information on curing them:https://www.gardeningknowhow.com/edible/vegetables/sweet-potato/harvesting-sweet-potatoes.htm

Yes, the tubers from ornamental sweet potato vines are edible, but they may not be as tasty as the varieties bred for food. Just make sure the plants haven't been sprayed with pesticides that aren't intended for edible plant use.
https://expert-hort.sws.iastate.edu/faq/view/id/191

I would cut off a small piece with the shoot and plant that, or else you will end up overcrowding the plant. It will root shortly.

I meant does it stop producing vines

The 90 days till maturity is the time from when you put the slip into the ground, not from when the slips were started on the sweet potato.