Is the Sharp 50FP1KA good for gaming?

Only casually. It has no VRR and no high frame rate support, so fast console games will show some judder and tearing. A gaming-focused TV at this size is a better fit.

Does it support Dolby Vision and HDR10?

Yes, both are listed. Dolby Vision helps on compatible Netflix and Disney+ content, though the panel's lack of local dimming limits how much HDR pop you get.

Can I cast from my phone to this TV?

Yes. Chromecast is built in, so you can cast from Android and iOS apps that support it, and Android TV has its own app store for streaming services.

What connections does it have?

HDMI, USB-A, an Ethernet port, a headphone jack and Bluetooth. That covers a console, a stick and wired networking, but check the HDMI count if you have several devices.

Can it be wall mounted?

Yes, it is VESA-mountable. You will need a bracket rated for a 50-inch set and the correct screw spacing for this model.

Is it a good upgrade over a 1080p TV?

For streaming and broadcast, yes: 4K resolution, HDR support and Android apps are a clear step up. If you mainly game or want deep blacks, a set with local dimming is worth considering instead.