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Weed torches are great for killing off the aboveground foliage of plants, but the heat doesn't penetrate deeper than a few inches into the soil. This is good because you won't damage tree roots and other soil life, but you also won't reach the tough root system of the periwinkle.

If you come back repeatedly to flame off the foliage every time it grows back, your plan might work. You will probably have to do some manual removal of the roots as well, though.

Yes, you can prune it back and you can also pull out any periwinkle plants that have spread beyond where you want them. Periwinkles usually spread if they're not pruned every year.

Yes, Periwinkle does retain it's green color throughout winter in most climates.

I know in my own zone 4 garden it stays mostly green with some areas turning a dark almost burgundy color. It recovers nicely when the weather warms.

Yes, you can trim your plants.

It seems like your plants just need a bit more time.

http://articles.chicagotribune.com/2012-03-29/classified/ct-sun-garden-0401-qa-vinca-thin-20120329_1_pachysandra-terminalis-common-periwinkle-bed

These can, often, be found in hanging baskets. They do best in this fashion, or a raised container, but yes, they can be grown just fine in container. This article briefly mentions this: https://www.gardeningknowhow.com/special/containers/hanging-basket-plants.htm

It will likely do poorly under a pine, as do most plants. This website offers a list of plants that can survive in these conditions:https://www.thespruce.com/grass-doesnt-grow-under-pine-trees-2152742