You can change your default web browser on Mac from System Preferences or from your browser's settings page.
Using the same web browser for everything is certainly doable, but keeping things organized between work and personal stuff ...
You can change your web browser's search engine through the browser's settings on your computer or the app or system settings on your phone.
The default browser isn’t always your best option: Microsoft might really want you to use Edge, but maybe you’ll get better performance out of Chrome or Firefox. On a Mac, Safari is rather limited, ...