External gate resistor calculation
Usually, you don't want much of a gate resistor when you're using a driver IC. Think about it. The resistor limits the current into the gate. The purpose of the gate driver is to push a bunch of current into the gate to turn it on faster. The two work against each other. I would start off with a set of pads populated with a \$ 0 \Omega\$ resistor. If you run into ringing during testing, you can swap out the \$ 0 \Omega\$ for \$ 10-100 \Omega\$ to increase the damping coefficient. It's hard to model and calculate this stuff with all the parasitics involved. There is no substitute for good testing in the application.