I've played a lot of the game, so I can probably answer some of your questions. But I'm not the dev (obviously), so I might be off on some things.
The Black Market doesn't really get new items in stock very often. It's mostly a place to act as a safeguard in case you sell one-of-a-kind items, as far as I understand it (if you do, they'll show up there.) And I think that shops in general don't restock too much? I'm not too sure about whether they do around your point in the game, but they don't really restock at all when you're as late into the game as I am (I've hit the level cap for the current update.)
A lot of your complaints seem to stem from you possibly lacking story progression. As you progress in the main story, new things get unlocked. If I don't know what to do next, there's two places I always go: The Fortune Teller, and the Bar. The barkeep will give you hints on ways to make the main story progress, and the Fortune Teller will give hints about specific characters' storylines. In this case, the Bar is probably the place for you, since I don't think anything like that gets unlocked from the side stories (besides maybe Nel?). If you're confused about what to do next even after asking the barkeep a couple times (he sometimes has multiple tips), let me know what he says to do, and I'll try to help you out.
I play on computer, so the lag you're getting might be a mobile-specific thing. Not sure if the game is super well-optimized for mobile? That's something Deimus would have to say.
I know that there's a way to increase your wallet cap a lot higher than what you currently have (via Fusion), so perhaps look into that? Again, lack of purchasables for you is probably due to lacking story progression.
IDK about the experience thing. I know that grinding underleveled enemies gives less XP, SP, and Gold, so you might just not have unlocked a sufficiently-difficult area yet. Also, there are Skill Point Books in various spots around the world, so you might try to look for some of those. I know that skill points don't directly correlate to levels one-to-one, so you might just be in one of the levels that doesn't give skill points.
I am certain that every gold nugget you get has a use. If you have so many that you don't need... I think you just might not have all the Accessories yet. Anything Silver can be upgraded to Gold, keep that in mind. Not sure about the Fusion book, I've never really put it to much use myself. I think it shows fusion recipes that you can currently make, but haven't yet, with just the first ingredient as a "known" and the other one as "???".
Arcane increases Spell Damage (although I think it also erroneously increases all attacks, including physical ones. I won't spoil what specifically said attacks are, in case you haven't gotten to that point yet. But it should be pretty obvious that it's physical when you see it.), Allure increases the chance that enemies will attempt to strip/molest Celica rather than attacking, and Willpower increases the success rate of attempting to remove an enemy that's currently grappling you. So, the longer you're in a grapple, the less chance you have to escape it.
Hope all this helps!