I cannot help with the processor and camera, but the battery is comparatively easy.
For most phones, the electrical interface is usually three-wire (plus, minus, thermistor referenced against minus). Some batteries have more wires; e.g. the iPhone 5S has a fourth wire, a serial comm line with the bq27541 battery gauge chip. You can extract the board from an existing battery and just replace the cell with bigger.
My first cellphone came up with nearly dead 500-or-so-mAh-as-new battery. I replaced the cells with 2.2 (or maybe 2.5?) Ah round NiMH ones placed into the shell of the original battery, protruding out, and wrapped in electrical tape. Voila, LOTS of standby and talk time.
Batteries without chips inside that would need to communicate are easy, it’s just mechanical adjustment of the case to fit them. It becomes tricky with the battery gauge chips, which need some individual care (or may lie to you and you have to suck it up).