I have a few comments, although I'm not as experienced as Mark Fulton. My comments are preceded by #####, and I've <snipped> liberally to conserve bandwidth.
Mark: Yeah, I'm old enough to remember inch-pitch stuff. My track racing career peaked in 1949 and 1950. First, let's clear up one thing: it's "skip tooth" not "skip link." Now then let's consider your questions.
1. I don't know if you should "care" about block or roller chains, but maybe you should know the difference. Look at the photo in the third eBay item, the inch-pitch roller chain. A block chain looks pretty much like that but with solid, shaped steel blocks replacing the rollers and inner links. ###### the appearance is VERY different, once you've seen one of each. The roller chain looks much like beefier modern chain, until you notice that it's only got one gap per inch, instead of two. The block chain is much sleeker at the same nominal size. <snip>
3. Because they're stronger, block chains were better on the track. Remember we're talking fixed gear drive here. Track racing requires starting sprints from a dead stop. Ever present, however slight, chain slop combined with sudden pedal impact could snap the weaker roller chain. Improved chain materials has made current roller chains stronger. And freer spinning ability means current roller chains are quicker and faster that the old block chains. ##### I haven't looked for data, but Rexnord.com is a major manufacturer of industrial chain, with engineering data for the chains they sell posted on the web. I'm too old to worry about breaking chains on my single. I suspect that Mark is right about improved metallurgy.
4. That I can't answer. ##### Warning: cogs for coaster brakes are just slightly larger in the threaded diameter than those for most bicycles. They will NOT interchange. Exception: Schwinn Paramount takes the track-standard 1.370" cog, but I'm told the Superior of that vintage used the coaster size. IF the cog in question has a radial slot, it is certainly a coaster cog, and will not fit a proper fixed-gear hub (except Superior?). The slot allowed replacing a drive-side spoke w/o pulling the cog.
One final note; of the two cogs pictured only the first one looks suitable for a block chain the "lumps" between the teeth on the second one look like they could interfere with the blocks. I don't remember the blocks being relieved enough to clear those "false teeth." ##### My Wippermann block chain has slender "waists," and just might theoretically clear. Using that combination would still be a kludge, and heresy if there were any options (like grinding away the lumps). But, I think it may be irrelevant: I'd suspect that a cog with "lumps" was meant for coaster bikes after they transitioned to roller chain. I could be wrong.
##### Two other differences: 1) My Wippermann block chain (Thanks, Ted Ernst) is only ~2/3 the weight of the same length of 1" roller chain. Substantially lighter, and to me looks more elegant. But, eBay prices are said to be much higher. 2) Block and roller chain take very different master links. Roller master links are little stubby things that just bridge the gap between adjacent rollers w/o gap, while block Masters are much longer, to bridge the sprocket tooth gap.
##### So, think that there are lots of wonderful attributes of 3/32 chain, whether block or roller: 1) They are heavier than 1/8" x 1/2" chain, so the bike has less tendency to float away. 2) They cost much more, so there is some exclusivity value (?). 3) You don't need near as large a stock of spare cogs and chainwheels, since there are few alternative final ratios relative to 1/2" pitch.
But, I'll still keep my one-inch block chain on the '38 Paramount, because it is the right thing for that bike. thanks, Ted!
hope this helps.