just put your PS4 in standby mode and let it download overnight
usually should complete overnight or within 24 hours

not so much when it's in rest mode, which consumes only 4Watts
you let it run a year in rest mode also the electricity bill is only less than RM10

has got nothing to do with attitude my man. they aint gonna give you public IP just because you need it. they have a package for public IP and you need to pay extra if you need it. CCTV can easily be reached from outside using dynamic dns+portforwarding.

anyway, for the NAT thingy,

NAT1 = PS4 connected directly with public IP
NAT2 = PS4 being within private IP segment, NATed once by your home router
NAT3 = same case as above, but NATed twice. This can be caused by few things, but most obvious is you have a second router. If you don't then it's probably the configuration inside your home router, where its either setting up a virtual gateway for redundancy or segmenting your network, or could be number of other reasons.

But NAT type alone should be a problem for any of your PS online session, as long as you have good latency/bandwidth. They are more relevant when you using Remote Play from the internet, where you client need to find your PS4 to connect.