Question 1: does this mean that any USB-C laptop charger with an output larger than 65W will be sufficient?
Yeah, pretty much. The general rule being that if the machine needs like 40W, a 65W PSU should be good. You don't want to load the power supply at its rated max as they often burn out somewhat fast in that case. So round-up, in terms of power (Watts). Do NOT go over on the voltage though, but given we're talking USB-C, the voltage is probably a fixed-assumption.
I personally have a lot of Apple gear. I buy only their 85W power bricks because they'll happily run my top-end MacBooks all the way down to my little MacBook Air. I've done this for years, I've never had a power issue.
Question 2: the charger that was included is not able to charge my phone, how do I make sure that the new laptop charger that I buy is able to charge both my phone and laptop?
I can only guess why it doesn't charge your phone. It may be the case that you have a device like an iPhone that expects a voltage presence on the USB data lines, which some USB power sources do not provide. I'd check the voltages on the USB pins to see if that's even the case. There isn't much detail to go by, so maybe your problem is as simple as your phone's USB cable is busted. Assuming it's a real problem, I'd measure those pins & write them down. You can adjust your question with what you find.