Not sure why the photos don't seem to be showing for you guys. They display fine for me, so I'll re-attach them below and see if that helps.
On your questions:
1) Yes, the photo you have is a Type 1 Original. A little waviness/rippling to the photo won't really affect the value, and could probably be pressed out if desired. Generally speaking, condition issues
that do not detract from the central image are not a big concern with news photos, and certainly not to the degree that they are with cards. The way I see it, a photo being in good condition is a nice perk, but with most vintage photography, chances are you'll never see another period print of that exact image to potentially upgrade to, so you base your decision to buy or not on the central image itself, not whether the white border around it shows signs of handling. Or in simpler terms, if it will produce a good scan, it's okay by me
2) You are correct that NEA stands for Newspaper Enterprise Association. It was founded in 1902 by Edward Willis Scripps and was one of the first news syndicates, handling distribution of news, features and comics to subscribing newspapers. Think of NEA as the parent company. In 1923 they ventured into photo distribution as well with United Newspictures, changing the name a couple years later to Acme Newspictures. This is why you will often see the stampings of both Acme Newspictures (the photo distributor) and NEA (the parent company) on the same photo. At the end of the 1920's, they also acquired Pacific & Atlantic Photos which added to their subscriber base and gave them a larger coverage area. In 1952, Acme Newspictures was consolidated with United Press, another Scripps-Howard photo distributor and they continued under the singular name of United Press. Prior to that consolidation, Acme had handled national photo coverage, and UP international, so after their consolidation they provided true worldwide coverage. (Thanks to A Portrait of Baseball Photography for all of the above info).
NEA was a big, dominant news syndicate, which is one reason you see a lot of their photos being offered. The other is that the group behind the various historicimages seller usernames on eBay has recently acquired and begun listing NEA's photo archives. So you can expect to be seeing LOTS of photos, of all genres, hitting eBay over the next few months (or years?)
3) what Mark said
4) Don't worry about stickers and such on the backs of photos. The reason those are there is that as the various newspapers' archives are broken up and sold off, the sellers have added bar-coded labels for keeping track of the thousands or millions of photos they are processing as well as "hologram" or other stickers to indicate which archive the photo came from. Some re-sellers make a big deal of the "pedigree" of the photo based on the sticker, but it really doesn't matter whether the photo came from The Sporting News, The San Francisco Examiner, NEA, or any of the other archives that have been broken up. Chances are, if you attempt to remove the sticker, you're going to wind up doing more harm than good, and nobody will thank you for it if you're successful unless, like Mark said, the sticker is covering something important (most of the time, the sellers of these archive photos have sense enough to not cover anything important).
5) Again, what Mark said. Also, as I think was mentioned in the other thread, some wire photo processes were simply better than others. Keep in mind that most of the time, the wire photos were published in newspapers, which inherently have HORRIBLE image quality compared to the original photos, especially in those early days. I suspect that having a wire photo that came through with less-than-stellar quality was not as big of a problem as we might normally think, and a skilled editor could touch up almost anything to make it good enough to print. I've seen a couple recently where they basically
completely redrew the main subject's facial features to improve the contrast enough that they would show up in print! I might also guess that some of those photos with wider-spaced lines making up the image are a result of a poor transmission the first time around.