It looks like a good build yes. I have two suggestions: for the motherboard you can go with the MSI gaming edge WiFi. It's a bit cheaper and has great features. For the SSD get either the Samsung Evo 980 (to get the PCIe 4.0 connectivity) or another cheaper model maybe?
Pc part picker always gives this warning with B550 motherboards. You should be fine now, manufacturers most likely updated the bios. If not, there is a bios flashback option on both the MSI board I recommended and the Asus you picked. It means you can update the bios without any components on the motherboard, which is quite handy.
For the cooler you can try with the one that comes with the processor and see if you're happy with it's performance and noise level. If it doesn't meet your expectations just order a better one (noctua makes great air coolers. They're not cheap but they're silent and good quality)