Can she deposit $1 on my Ledger device in 2024, so that I can withdraw profits to her account when EU regulations don't allow me to withdraw?
You can deposit only Bitcoin and other cryptocurrencies in your Ledger hardware wallet, including some stable coins that are supported, and you can generate as much addresses as you want.
You can't deposit any fiat currencies from bank or anywhere else, unless you purchase Bitcoin first, either directly with cash or online using exchanges.
Better check your local regulations for more detail and it can be very different depending on specific country.
Or can a Ledger device only be connected to 1 person?
One ledger can be used for several people, but only if you generate multiple passphrases for each person, or if you reset device and import separate seed words each time.
This can be confusing sometimes, so I suggest getting separate devices that are not so expensive.