Not really. Samsung was the first with this, but their reasoning had absolutely nothing to do with security. It was because their phones slowed down over time and their solution was to give users the option to reboot it at specific intervals. You could even make the argument that the Samsung solution is still the superior solution because you get to set the interval.
Because it's an effective tactic against exploits that can't survive a reboot, which is somewhat common from my understanding. The idea being that police can confiscate your phone and just keep it on and charged until they can buy or develop an exploit targeting your current device and software.
I was admittedly confused about this distinction at one point too. It's a trade-off (although few people effected by this own phones with truly free, user-respecting soft/hardware in the first place).
As the GrapheneOS docs note, the feature is better implemented in init and not in system server or the app/services layer like Google has done here? Though, I am sure Google engs know a thing or two about working around limitations that GrapheneOS developers may have hit (in keeping the timer going even after a soft reboot, where it is just the system server, and the rest of the userspace that depends on it, that's restarted).
Huh, I have GrapheneOS and I never noticed it rebooting. (And when i manually reboot, the "BIOS" prevents it from booting without acknowledging that I'm aware it's a non-Google OS, so how does it work?)
The feature is not enabled by default. Also, the boot doesn't wait for you indefinitely - it just gives you a few seconds to glance the checksum and halt it, before it proceeds automatically.
You don't have to acknowledge anything. The boot screen shows a warning which you can interrupt. If you don't do anything it'll continue to load as normal.
No. Play Services is Google's way to make Android closed source. Many new features don't get implemented in Android, but Play Services. Many apps don't work (correctly) without Play Services.
Being closed source is not the goal. Update speed, consistency across the ecosystem, and feature development speed are key reasons things are implemented via play services. Also dependency on google services, but that's not relevant here. AOSP is greatly improving in its ability to tackle these things, so the choice to implement things in play services won't be as compelling as it is today for things not ultimately tied to Google.
Play services is how Google delivers many Android updates now so that all users can get security updates without waiting for the device vendor to publish it for each device.