Upload limits of 1 MB, 2 MB or 5 MB are everywhere on government and university forms, and scanned documents blow past them immediately. Here is what actually works.
Almost always, it is the images. A PDF made by scanning or photographing pages stores a full resolution picture of every single page, usually at far more detail than anyone will ever look at on a screen.
A PDF that was exported from a word processor is a different animal. It is mostly text, it is already small, and compressing it will save you very little. If your file is under a megabyte already and a form is still refusing it, the problem is probably the page count or the form itself, not the size.
Compression works by redrawing each page at a sensible resolution. The trade is real and worth knowing: the text stops being selectable and searchable, because the page becomes a picture of itself. For a form submission nobody minds. For a contract someone needs to search, send the original.
Yes. Balanced is chosen to stay clearly readable in print. It is selectability you lose, not legibility.
No. The whole thing happens inside your browser, on your own machine. Turn off your wifi after the page loads and it still works.
Then your PDF was already efficient, which usually means it is text rather than scans. Compressing it further costs quality for almost no gain.