Can I use a 20w fast adapter (Type-C to lighten) for my iPhone XR?

Yes. You can charge an iPhone, iPad or iPod Touch with any quality USB-A or USB-C power source and matching cable. Essentially any Apple power source and cable that fit into the connectors at either end are compatible and safe to use. There will be performance differences, with USB-C faster than USB-A to charge, but they will all work (except that a USB-A “cube” doesn’t have sufficient power to charge an iPad). For an iPhone 12 or later you can fast charge using a 20 watt or higher power USB-C that meets the PD spec. The Apple 20 watt and higher is PD compatible, but not all 3rd party power sources are yet. For more info, see:

When to charge your iPhone or iPad - Apple Community

No, the phone will draw as much current as it needs, a larger wattage charger won't hurt it.

Yes.