How do I install Zoom on Macbook Air (2015) with the latest Big Sur? Is there an app?

Download the app from Zoom and install.

https://zoom.us/download

Sometimes zoom doesn’t work on browsers like safari. I tried logging into a meeting on safari and it said “ Please update to the latest version ...”

Yeah, try it on Chrome, ect.

Then you have other issues you need to resolve first. If you cannot reach a website that means you have a questionable internet connection. Can you visit other websites? Have you tried a different web browser like Firefox or Chrome? Do they work?