(1) Does Hilditch and Key / Turnbull & Asser manufacture shirts in precise neck and sleeve sizes? If not, what is the typical sleeve size for 16" neck?
As VersaceMan wrote, H&K sell their shirts in two sleeve lengths per collar size, whereas I've only ever seen T&A shirts come in one sleeve length per collar size. I would think that an H&K 16R would have 34 or 35-inch sleeves, while a 16L would have sleeves about two inches longer. A T&A 16 would probably have 36 or 37-inch sleeves (the idea being that you can shorten sleeves, but you can't lengthen them). H&K or T&A should be able to tell you for sure if you call or e-mail.
(2) Do H&K and T&A shirts cost more here in the US compared to in the UK?
H&K shirts in the US start at around $195. They start at around Â£70 in the UK. If my math is correct, VAT in the UK is around 17.5%, so the ex-VAT price for H&K shirts would be around Â£59.60. At 1.83 USD per pound, that translates to around $109 per shirt. (All math is approximate.) The situation with T&A shirts is comparable.
(3) When do H&K and T&A have sales in the US and UK?
US retailers typically have a couple of big sales per year, one during mid-to-late winter and one in mid-to-late summer. I don't know about UK retailers.
(4) In what ways are H&K and T&A shirts superior to those tailored by Jantzen?
I've never seen a Jantzen shirt, so I can't compare that to H&K and T&A. However, I can tell you that H&K and T&A RTW shirts really aren't anything special. The T&A collar shape is unique and classic, and both brands often have interesting fabrics. The overall quality of the product, however, isn't really commensurate with the price.