Hi Nevetsb54
welcome to this Apple (user-to-user) Community! Your father is indeed fortunate to have your assistance!
Re: "How to get sound alerts with text messages and alarms while phone is in assistive access mode?"
Am no expert in this area, yet your request to the community deserves some response
I understand your father's need to hear alerts and alarms with Assistive Access on his iPhone
You can adjust various settings to customize the Assistive Access apps,
and
you can add other apps (like the Clock app) if you want to:
While some settings can be changed within Assistive Access, for others you will need to exit it.
Apple support's article may help: Change Assistive Access settings on iPhone - Apple Support
and
there's a useful: Assistive Access User Guide - Apple Support
Note: To see all the detailed "How To" info : You can click "Table of contents" at the top of the Welcome page that opens from the link above
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Also: If you wish: Siri can be used for many things, including to announce messages (and calls)
(Seems the more you use Siri, the more Siri learns to tailor what is needed)
See: Change Siri accessibility settings on iPhone - Apple Support
Eg: says:
"Announce calls and notifications for specific apps
You can have Siri announce notifications and calls from apps like Messages on your iPhone speaker, supported headphones, when using CarPlay, and on MFi hearing devices.
- Go to Settings
> Accessibility > Siri, then turn on Announce Notifications on Speaker. - Tap Announce Notifications, then for each app, choose whether to announce all notifications or only time-sensitive notifications."
All the best :-)