1. I'd give you 2x the amount of time off immediately, the next morning. Minimum 2 hours. More than that, I'd ask if you'd prefer to shift your workday later or find some other flexible arrangement.
I have fought management at some places really hard when they said a word about someone's planned work bucket not getting done after being paged as much as OP has in a week. I've made it clear it was management's fault, not yours.
2. Absolutely not. You'd be given the option to get rotated off Pagerduty as soon as your life was disrupted. I'd personally take over your shifts if I couldn't find someone on our team who was willing to take over.
3. This is SRE priority #1 and I felt terrible for OP. We cannot run a marathon if we're always sprinting out of bed for crap. Alert Fatigue is real https://www.pagerduty.com/blog/lets-talk-about-alert-fatigue...
4. Bingo. So, the whole organization has to reduce velocity so we can pay back the debts. If the CTO doesn't totally empathize with this, they're going to trip over their own shoes.