How to restore new Mac mini from iPhone backup

You don't. How to back up your iPhone, iPad, and iPod touch - Apple Support

IF you're upgrading to a newer Mac mini, you should have an option to migrate from your old mac mini.

Not all apps are universal for all Apple devices.

You cannot restore a Mac from an iPhone backup. It doesn't make sense. iPhone apps don't work on a Mac, and any data you need on your new Mac would be synced through iCloud or other online service.

You should be making backups from an old Mac, and use them to restore the new Mac. If using time Machine some apps that allow it can be restored.

Restore your Mac from a backup - Apple Support

There's also the migration assistant to move data and apps from one Mac to another.

How to move your content to a new Mac - Apple Support

The other option, is to create a clone of the old Mac and use that to restore the new Mac. but yes in general, computer Apps need to be re-installed from source, and many times you need to supply the registration key you got when they where purchased.

No. As we mentioned, Migration Assistant, or a Time Machine Backup will let you restore most data and Apps that allow direct migration.

For others, for example Microsoft Office, that require a product key to install, they will need to be re-installed.

I would start with a backup or Migration assistant, and from there see what still needs to be re-installed.

Full day depending on how many apps you're trying to download.

Read my last sentence, if you don't understand the answer is No.

You cannot restore a Mac from an iPhone backup. It doesn't make sense. iPhone apps don't work on a Mac.