[Google Pixel 7 Pro] roirraW "edor" ehT:
Hello, and welcome to XDA!

Yes. See what I say two answers below about this month's update, though, before deciding.

No, no particular risk of any kind of brick no matter which way you do it.

Yes. It would just be a waste of time to root your phone, then update and root it again. Keep in mind that another regular monthly update from Google is due anywhere from tomorrow to more likely next Monday early afternoon GMT -0500. It's usually the early afternoon on the first Monday of each month, but in weeks that have a national holiday (today), it's common the update comes out the following week instead, although there may be a slight chance that the update will just come on a non-typical day (tomorrow).

So it's up to you, but you could go ahead and take the OTA to June's update, then wait for July's OTA whenever that comes, and root that. It's only a little bit of wasted time if you root sooner rather than later, though, so it's really no big deal no matter which way you choose to do it.

After you toggle OEM unlocking in Developer Options, then follow the directions in the first posts in this thread to unlock the bootloader, the bootloader will stay unlocked until you explicitly give the command to lock it (which could include the option at Google's official flash site to check the box to re-lock the bootloader). See instructions in the first posts for how to un-root to get an idea about what's involved in re-locking your bootloader.

But you should never re-lock your bootloader once you unlock it, except for if you're returning it for RMA (although it's still not really needed for that), I also always re-lock the bootloader after returning to 100% non-rooted stock before trading a phone in or selling it.

IMPORTANT NOTE: Unlocking the bootloader will factory reset your phone. There's no way to get around that. So you should unlock the bootloader before getting too invested in how your phone is set up.

No. Also, you can go ahead and unlock immediately, and then take or sideload whatever OTA you want - which, Verizon build or not, will not be ever capable of re-locking your bootloader just by flashing it.

No official Google firmware can turn your factory carrier-unlocked (and bootloader unlockable) Google Edition Pixel into a Verizon Edition. Note that from the other side of the coin, there are zero advantages of having a Verizon Edition phone other than possibly getting good deals on how much it costs, or financing over time, or trade-in values, but IMHO, I'll always avoid getting carrier models of any device, if I can help it.

Yep. The builds indicate what carrier the build is optimized for. The Global will still work, just that there's a chance the Verizon build will work better. Note that occasionally, the Global build might come out on the proper monthly first Monday, but sometimes additional builds don't come out until days or a week or so later, and we usually don't know if an additional build will come out until it just suddenly does.

And sometimes there won't be builds specific to any carrier, just the Global build. As I said above, it'll still work for you.

Not problematic (just spelling out to address each of your points).

I'm not an expert on this area, but the Global builds will still work for the Verizon specific radio bands. It's just that the Verizon builds might work just even a little better. Even this is arguable. I've seen some users with such-and-such a carrier who the Global build worked better for than the carrier-optimized build.

Good luck and have fun!