Not getting missed calls or text while Do Not Disturb is on

I just got an iPhone 14 pro max. I have iOS 16.3 on it (so ignore the note below my questions saying iPhone 5, iOS 10). My previous phone was quite old. The thing that I can’t figure out on my new phone is why this phone doesn’t show missed calls and text messages when Do Not Disturb is on. Let me make it clear, I don’t want my phone to ring or ding when I get a message and do not disturb is on, but it would be nice to be able to see the missed call notification and to still be able to see/read my text messages when do not disturb is set. My old phone I would be able to see missed calls and from whom, I was also able to see and read text messages while do not disturb was on (but the phone wouldn’t ring or ding). How do I set this phone up so I will see the missed call or text while do not disturb is on, but my phone won’t ring or get a chime.

My second question is, will this new phone ring if someone calls me twice (from the same number) within 3 minutes when do not disturb is on? That was a nice feature on the old phone, so people could still contact me if it was an emergency. I’m worried that this might no longer work on this phone. Is there a setting to enable this, calls from the same number in 3 minutes will be allowed to go through? If there is, I can’t find the option in this new iOS.

Thanks for any help on these 2 questions.