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It is very possible to have different color variations. This can be affected by soil nutrient content, as well as temperature and humidity. Don't worry, this is actually happening, and is a neat sight to see.

Growing zone is 5-9. Yes, I did find reports of them growing in large containers (20 gallon or more). They do have a large tap root, so this is often not good for container growth so the deeper the container the better. Less flowering is reported with container plantings.

https://www.gardeningknowhow.com/ornamental/shrubs/mountain-laurel/mountain-laurel-growing.htm

The root system is shallow but with a deep tap root.

I cannot make any recommendations on the safety of your removal method.
I would suggest checking with a qualified tree removal expert.

Although a lot of the information says it will grow in part shade, it will definitely bloom better if it is in full sun. Obviously, with a plant this age, you're not going to be moving it into a sunnier spot, but perhaps there are shrubs or trees around it that could be trimmed back to provide more sunlight.
Second, don't fertilize it, especially not with nitrogen-high fertilizer, such as lawn fertilizers. The plant is a legume, and has an internal mechanism that permits it to fix nitrogen in the soil, some of which it uses itself, and some of which can be used by other plants. Many plants are adversely affected in terms of blooms when they are over-treated with nitrogen.
The mountain laurel produces flowers only on one-year-old wood. Pruning now, getting out weak branches, trimming off long, thin stems, and general cleanup should propel it into blooming on that new wood that will sprout after the trimming.

You may be better wintering over in a sheltered garage or shed until spring.

If it is small you may need to insulate the container with some insulation. A small container may dry out, so check it throughout the winter. A small amount of moisture may be needed to keep the soil from drying completely.

Many mountain laurels, Kalmia latifolia, are 3-4 feet tall. I did find dwarf one called "Tiddlywinks" that is 2-3 ft tall and wide. Your site may have too much sun for this plant. Other options are the dwarf laurels "Elf" and "Minuet". It is usually grown with morning sun only so be extra careful to give it the water it requires - 2 inches each week. I would do a soil percolation or infiltration test to make sure your soil drains fast enough as laurel is won't do well in poorly drained soil. https://extension.tennessee.edu/Williamson/Horticulture/Consumer%20Horticulture/DIY%20Soil%20Drainage%20Perk%20Test%20for%20Your%20Yard%20(2016).pdf
https://www.gardeningknowhow.com/ornamental/shrubs/mountain-laurel/mountain-laurel-growing.htm