Yes, commonly referred to as a “battery emulator” in EE labs for mobile devices. Some are lab grade test equipment from big name vendors, and some are home-grown concoctions which use a power supply, capacitors, and adjustable load to shunt the power when the device tries to “charge” the battery. If a battery charging circuit is running, it’s generally not enough to just provide a DC power supply, it actually needs to be able to both source and sink current. But if the battery charger can be disabled, then a high current power supply, lots of capacitors, and a good short connection can be enough to replace a battery for a phone/tablet.

Sure, it must be possible. You just need to give the right voltage to the +/- pins, and most phone batteries have at least one or two additional pins which you'll have to reverse engineer. Usually a thermistor for temperature reporting, which you'd replace with a fixed resistor / voltage divider to report a constant temperature.

Apparently some manufacturers put the phone's NFC coil inside the battery instead of on the phone's back housing, so there could be a fourth pin for that. Or perhaps the battery contains its own microprocessor that answers a DRM challenge from the phone specifically for the purpose of blocking out third party battery manufacturers. Etc. etc.

Still there is the problem that the phone might have peak power usage above what its charger can provide, so you'd have to use a wall adapter with a higher amperage rating.

This sort of thing exists! I use something like that with my DSLR for a webcam. It’s great, there’s no real battery involved, it’s just a power cable with the end shaped like a battery.

Depending on how dumb the battery controller is, all it takes is pumping the right voltage back into the appropriate pins.

You literally can connect 5V instead of the battery (and a capacitor for some more stability) and the phone will gladly take that and power on.