[Google Pixel 7 Pro] simplepinoi177:
Sorry I can't answer much of your questions; I just wanted to answer what I can and hope to bump your post a bit so maybe it can be answered by experts better than I.

I am not certain as for your first question (so please just take it as my opinion and don't base further action from it), I imagine Google anticipates such actions that by sideloading OTAs would cancel/invalidate whatever partial/paused OTA is currently being downloaded. If anything, I imagine it would only be troublesome if it was in the process of "installing", but if you paused it early on, most likely it was still downloading and/or I doubt you could pause it once it was actually in the middle of installing.

As for your second question (again, just my opinion and do not base further action from it), I imagine OTA's, although incremental, carry-over and/or include whatever improvements the previous OTA's had and it merely modifies & works-on the core system and much of it isn't really touched outside what the OTA patches so applying each update step-by-step isn't really applied to much of the core system. In the end, what I'm implying is that if I were in your position, I, myself, would not apply each OTA from what version you are in to current -- I would merely install the latest OTA only.

Honestly, if you are concerned with the incremental differences OTA's apply and are going to sideload them anyways and you mentioned you'd like to update it quarterly and prefer a "single update", you should consider flashing the full factory images instead of the OTA's. You have to open up a command prompt and run commands anyways (also you would need to if you plan to re-root), the major differences is you run commands in the bootloader mode (than recovery mode) and run a few more commands (fastboot than adb); one other important addition is you

MUST

remove "-w" from the flash-all script to keep your data -- but that's basically it. Again, this case & opinion only applies if you are sideloading OTA's, un-rooting and implementing the (very fairly slow, although it's been announced it has been more streamlined and process time has been cut down significantly) System Update in the OS would not need you using the adb command (necessarily) and downloading & applying images.

One other thing I might mention since you mention "Pixel OTAs + retain root" (even if it seems you know this info already, but take it as a reminder if that's the case) is you are unable to apply the OTA through System Update if you are rooted as well as once you apply the OTA (or Factory Image), you will lose root; there is (currently) no way to apply the OTA and "retain root" -- it must be re-applied.

As for your inquiry about blocking the OTA check/auto-download, roirraW "edor" ehT touched on the topic and pointed to a post that might be applicable back in post #1318. It might do and/or at least point you in the right direction.

Lastly, yes, sometimes the firmware & OTA updates break things related to root and bypassing root checks, but you can always count on it being reported/discussed here and can keep updated on things and its progress here -- but such is the risk of rooting and keeping the device up-to-date. Depending on the "damage", it's usually dealt with swiftly enough...the great developers that work on aspects of this device, Android OS, and Magisk work ever so diligently...

I could be completely wrong, but I don't believe you need to be unrooted to sideload the OTA; you only need to be unrooted if you plan on using the System Update in the OS. BUT, regardless, in all options, root is lost and must always re-root afterwards. As I said with taysandman, I implore you to seriously consider still updating using the Full Factory images rather than sideloading the OTA merely because the Full Factory is a superior update (@roirraW "edor" ehT explains it best) as well as sideloading the OTA is not that much different or far-fetched from updating using the Full Factory image (both have to download images, open a command prompt, run commands, and you'd have to open/run fastboot to re-root anyway) -- the only big differences is it being done in bootloader mode instead of recovery, fastboot commands instead of adb, and you must modify the flash-all script before running it.

Apologies for the wordiness, but I hope it helps...