Do you mean, 'nerdish?'

Carriers retain recordings and the associated metadata. In a very real sense, it is not 'on your phone.' Except when powered off or out of range (of any cell tower), your carrier is in continuous contact with your device, even when you are not using it. Via the cellular network, your carrier constantly updates (or syncs) with your device, and when you 'roam' away from a cellular network, signal degredation is often a gradual process, during which time you may receive text messages, but the bandwidth needed to support a phone call (or voicemail) may not exist. Does this make sense?

It's stored on a server managed by your cellular provider (AT&T, T-Mobile, Verizon, or Sprint). Most other US, "providers", are Mobile Virtual Network Operators (MVNOs) that buy bulk minutes from the actual providers that have physical network infrastructure.

That server could be at the provider's data center or stored on, "the cloud", which is just a server hosted by a 3rd party (AWS = Amazon Web Services, Azure = Microsoft's version of AWS, and many others) that the provider leases server and storage capacity from.

They usually have a formula, deliver now if possible, if not try again in 5, 20,60 minutes etc, But it does depend on traffic.

I am a software architect and have been in the field for quite some time... I had to ask a friends kid why my iphone won't rotate because I could not see the lock on the pull up menu.

do not feel bad.

Missed call notifications come from a completely automated web based application that sends you an email message when the user doesn't answer an incoming call and the caller doesn’t leave a voice mail message.

Satellite transmissions travel at or close to the speed of light. I don't think it's anywhere in time or space for long. I would imagine it's software from your carrier that stores the message and delivers it when you're in range.