Hello hodograph,
Welcome to Apple Support Communities!
Congrats on your new phone!
We understand that since you've received your phone you've missed several SMS text messages and were unable to make phone calls without restarting the phone. We're happy to help!
Ensure your iPhone is updated to iOS 14.2. We can help with that. Let's go ahead and update your iPhone first. Here's the article to help out: Update your iPhone, iPad, or iPod touch
Before you update, we suggest making sure you have a current backup. It's always good to keep a current backup to keep your data safe. Here's a link to help complete a backup on your iPhone:
How to back up your iPhone, iPad, and iPod touch
Once you have a current backup and your iPhone is updated, let us know if you're still experiencing the same behaviors.
Thank you for using Apple Support Communities.
Take care!