1) yes. Root is like giving you administrator privileges to do more with your phone. It doesn't really change the look, just how the apps work. Think of it like when Windows pops up and asks you to approve an action and sometimes requires an admin password, it's sort of like that. Apps must be explicitly granted root access by you and you should only grant root access to apps your trust.
2) It is my understanding that Google Pay does not work with an unlocked bootloader (required for rooting), but there are ways to trick the phone into thinking that it is not unlocked/rooted. I believe it is an addon module for magisk.
3) Updates won't work. Because the phone is modified, you can't simply take the update as normal when it comes out each month. The update process is a bit different but you can still get updates, sometimes it involves unrooting, taking the update and then rooting again.
4) there are loads of guides for how to root. This one came up in a quick Google search: https://www.xda-developers.com/google-pixel-3-unlock-bootloader-root-magisk/
All that being said, I haven't rooted a phone in a few years (not since Pixel 1). The methods have changed quite a bit as SuperSU became less popular and magisk became the go to for root access. You mentioned you're new to Android and while tinkering with things is a lot of fun, understand there are risks. You could brick your phone or be without it for hours or days if something goes wrong.
A few other notes: unlocking the bootloader requires a full wipe of the phone. You will lose all data. Some other apps won't work with root/unlocked bootloader. Banking apps, Pokemon Go, et al will not work if Safety Net fails, similar to Google Pay.
I haven't seen any videos about getting Call Screen working outside the US, but I haven't really been looking, not sure if that is a valid claim or not. Regarding Android Auto, does that not work in Australia? I don't know if root is need to achieve that.
