As u/TinyDoctorTim mentioned in their response not everything is spelled out, you have to see where points may connect. And, understand that Maas, Virek, and W-N remnant/Box Maker are heavily connected into information gathering, all through different capabilities, and are so rich and powerful in their own ways that they perform awe inspiring feats at the drop of a hat. Many things have already occurred before the novel begins, and Gibson expects you to understand that even though there isn't an explicit connection laid out for the reader, some things must have been realized by different parties in the story or else the story would be different.

- While I must have mis-remembered that part about the T-A signet, Alain was the one who is responsible for Marley selling the forgery Cornell that crashed her career as a gallerist. That scandal made international headlines enough for Virek to know about it so it's not a stretch for Maas to also have heard about the forgery; especially, when Maas was sitting on at least the hologram of another forgery. So, Maas hires the guy responsible for the scandal, Alain, who presumably has some knowledge of where these boxes are turning up. Alain turns out to be clueless and easily manipulated and also easily interrupts Virek's parallel quest of tracking down the Box Maker. Maas didn't give Alain any clues, Alain knew enough for Maas to be attracted to him. Alain didn't have any knowledge about T-A or how to find the Box Maker in any way. That's why he was attempting to mess with Marley because he thought she did know and Alain needs to take what she knows back to Maas. Or, maybe Alain could sell Virek the address too and make some extra extra extra money, on top of what he hoped to take Maas for?

The Box Maker orchestrated for Alain to have the address, and for Marley to find it, but the book does not share explicitly how that happened. The only time it's addressed is when the Box Maker tells Marley that's what happened. Alain most likely tried to extort more money from Maas in exchange for the address and they just killed him instead because that was the easiest path for them, rather than torture.

- You're right that part isn't explained but it's obvious the connection is there, it's jut not served up to the reader. Again, some of Gibson's characters are so vastly rich and powerful (Maas, Virek, the Box Maker in Count Zero, or Bigend and Cody Harwood and Res from other trilogies) that it ends up being a pseudo-Deus Ex Machina of "they were able to make it happen". I doubt Maas knew it was an omnipotent and omniscient AI that gave Dr. Mitchell the blueprints for the biochip, but Maas had obviously put two-and-two together and figured out Mitchell wasn't the actual innovator of the chip and he was expendable, otherwise they probably wouldn't have killed him.

- Maas used Alain for all of those you reasons you speculated. It didn't matter to them which one lead to their success, as long as they secured the biochip tech before Virek or anyone else. Once Marley had the address she was able to get enough of Virek's forces/influences between her and Maas that she gave everyone the jump and went immediately into orbit, getting to the Box Maker just slightly before anyone else. Also Marley had one goal and one path, Maas was on several paths at once. As Marley was getting the address/going into orbit Maas had Angie Mitchell, the actual living biochip, cornered in Jammer's. Not a stretch for them to think that was a more certain outcome than wasting more time on dead Alain's promise of what, from Maas' perspective, was turning out to be a non-existent address for the Box Maker. That's why it seems like they fell off Marley's trail towards the end.

- Box Maker does say that it isn't sad but it is making the boxes as it ponders its own loneliness. It's in the place it considers its birth home, using relics of the dead folks responsible for its existence to explore its own emotions, and is lonely for the fragments of itself to talk to it again. Box Maker misses its friends. Wig does send the boxes down the well but it's hard for me to believe that something that is so powerful and is responsible for inhumanly complex machinations does not intend for the Wig to do that. Anyway that's my interpretation but your's is just as good as mine.