I'm afraid I'm going to start a disagreement here, but so be it. Answering the questions in order.
I thought I'd read about headspace issues and neck-sizing brass only for these rifles somewhere (?)
Yes you have, but they are (marginally at best) related only. Rimmed .303 cases headspace on the rim ONLY
. Nothing in front of the rim has diddly/squat to do with head spacing
, but it does have everything to do with neck sizing
In addition to headspace there is a separate issue, namely "generous" chamber dimensions. Let me clarify. the neck & shoulder area of many No1 Mk3 rifles (SMLE's was intentionally made "loose (read sloppy)) so dirty ammunition could chamber in dirty chambers during trench warfare. Because of this "extra volume" Brass should be customized to the chamber of that rifle for longer case life.
The point being that neck sizing & headspace are two different issues & should be addressed separately.
To check headspace I suggest getting the "Coin Type" gauge from Okie Gauges. they are inexpensive, easy to use & utilize the correct dimensions (which are NOT SAAMI). Headspace is a bigger problem with a non-matching bolt, BTW. A matching one is probably fine.
Whatever the gauge is called it should measure an 0.074" gap. (Okie call it a FIELD) The British did not use the SAAMI GO, NO GO & Field
specs they just had a min & a max.
Since it's a rimmed cartridge, are these potential issues related to worn lugs/raceways?
Nope not a one, BUT....
The Savage made No4 Mk1* guns used a simplified bolt release & that CAN be a problem if it's chipped or worn. Check the edges of the cut in the bolt head & the actual rail it rides in. It might be, but isn't guaranteed to be a problem. If the bolt head ever jumps out, even once walk away its bad & effectively not usable. The edges of both the bolt head cut & the rail it rides in should be well defined & not chipped or rounded.
it looks like somebody painted it black? if so that is not the correct finish.
It might be. Many Enfields were actually painted black. Many more were originally blued or (more likely from the '43 date) parkerized by Savage. Those might well have been re-painted, or painted by other owners such as South Africa where huge numbers of the Savage no4 mk1*'s were sent.
Does the rifle have a "birds footprint in a "U": anywhere on it? If it does it was once South African property.