Greetings from Virginia!!
Your initial efforts and pics look great.
You will not be disappointed with THSC seeds, I promise you that. I am growing his orange, chocolate and red habs, morouga red, fatali, and paper lantern. They are all going like gangbusters.
Purple stems do not necessarily mean light-related stress. Purple leaves do....if your leaf tops turn purple, they are getting too much light. For instance, here's a pic of a, I believe, red hab a few days after transitioning from a T12 to a T5. The T5 system is much, much stronger and threw my entire seedling collection into a state of collective shock. Gotta be really careful with T5 HO lamps.
Purple stems just indicate some type of shock or stress, which could include: too much water, recent transplant or up pot, too little or too much fert, and of course, too much light. My experience FWIW is that purple stems indicate nothing other than general stress, and should just be ignored, as green vs. purple stem doesn't seem to have any impact on plant growth over the long term.
You can grow a pepper in almost any size container, but if the container's small, you will just get fewer and smaller pods. IMO peppers "want" a container to grow in that's a typical 5 gallon garden container size, that is, 11-12" wide and 11" deep. Anything smaller than that and they will start yielding less and yielding smaller. As far as going larger, it may help a little, but you quickly hit declining marginal returns. A 7 gallon pot might give you marginally better results, but larger from there will probably make no difference and will be a nightmare to keep dry and unmoldy. The 5 gallon pot is really the best choice if you are seeking maximum yield in the most contained space. A 3 gallon pot will get the job done but you wil not get maximum yield from most pepper plants in that size container.