Will my phone still work?

You can get all those parts replaced. Just no touch ID at the end because the phone only accepts the home button that came with the phone to have working touch ID.

So basically you will need to get the following:

- Screen with preassembled parts (home button extension cable with Metal plate, earpiece speaker, front camera assembly)

- Replacement battery

- Replacement home button

iFixit sells all these parts and honour their warranties very well. You can alternatively get these fixed by a independent mobile phone repair shop or buy the parts from somewhere like eBay / etradesupply and etc if you want to get them cheaper for DIY. Make sure you are buying from reputable sellers and are getting the right parts. Don't go too cheap or you risk getting faulty / DOA parts (though the chance of DOA parts are still there on reputable sellers).