I wouldn't worry too much as (as you said) it may have just been a one off, however, do keep an eye on it. Fairy eggs are fairly common with pullets just beginning to lay and as hens get older their shells get thinner. Definitely keep on providing oyster shells on a voluntary basis. This article...
Supplemental lighting is often used in commercial environments to stimulate egg production during months where day light levels are lower, as you say. Is this detrimental for your birds, as they do not have a break from laying during the cooler months of the year, possibly even playing a part in...
Hard to label him a pattern, however your other EE's could be called red partridge. He looks to be slightly laced, but if he was a pure breed, it would be deemed very poor-quality lacing.
Looks like Tamari has been crossed over several generations. That would explain the pink feet (recessive over slate) and four toes (recessive over five).