Can I use more than 5V/1A without USB PD negotiation?
Can I just put two wires into the USB-C port on the device, giving it 15V without any warnings

Nope. That is a good way to kill devices.
Voltages above 5V require active USB PD negotiation. And yes, you can expect that the receiving device needs to switch the proper power path on.

how can I tell the device it's OK to take 3A from the 5V charger

Read USB-C specs: There is a pullup resistor, and one value is reserved for 5V/3A chargers. This allows drawing up to 3A by just measuring a voltage instead of the more complex USB PD protocol.
Warning: There are USB-A-to-C cables with this resistor value in the wild. These are not unlikely to cause damage if your device tries to pull 3A out of a PC or 1A charger.