This was incredible feedback, thanks so much for taking the time to write it out. I've implemented 2, 3 and 4. You can now directly link to pages[0] and it'll auto-expand all boxes. The icons are intended to show whether the sequence has a code submission attached. There's now a popover attached to them to explain this.

1 will take some design work, and I've only got an hour or so to work on it now. I definitely agree however that a 'submit' button on a search is essential.

[0] https://oeis.femto.dev/A000045