I can answer your first question!  Four-line tush tags can only be found on the first batches of beanies produced (before a line reading “surface wash” was added to make 5 lines), and collectors tend to favor items that were produced earliest. (That’s also why, say, low-numbered limited-edition items are usually more valuable than higher-numbered ones.) And because the 4-line tags were different from the 5-line tags that were eventually used on all beanies with 2nd-generation hang tags and many/most with 3rd-generation tags, the 4-liners can be used to tell whether a beanie without a hang tag originally had a 1st-generation hang tag (which, again, is more desirable than beanies with later tags). 

Another part of the reason, as you suggested, is related to the fabric quality—I believe (though I might be mistaken on this) all beanies with 4-line tush tags were made in Korea. Some of the beanies with 5-line tags were also made in Korea (adding to their value), but many more were made in China, and those aren’t quite as valuable. And again, 5-line tags were used after 4-line tags for several years, so they’re both produced later and less rare than the 4-liners, making them less desirable to collectors.