As for the secure use outside your home, see if you can install TailScale on that NAS. I use it on mine, it’s like having a Wireguard VPN but you don’t have to mess with port forwarding. The only downside is that to connect to your NAS from outside your LAN, you’ll have to be on a device that’s also running TailScale, but if it’s a device you own that’s easy to set up.
You don’t have to power the HDD via the motherboard, I’m 99% certain. No modern PC I’ve ever seen requires this. Your manual is ambiguous about connecting an HHD - it doesn’t explicitly say connect the power to either mobo or PSU which sows confusion. Furthering the confusion is that there are two SATA power connectors but those are not for 3.5” drives, they are for low-power bs like card readers. But big power hungry drives must be connected to the PSU directly. (Check your 10TB HDD and take a look. If it actually is connected via your mobo, you could try re-directing just the power to your PSU and see if it works (it will)).
For your new HDD, just see if there’s a 4-pin Molex from your PSU that is unused and get an adapter, or get a splitter for one of the existing SATA power cables from the PSU and stick it into the HDD, alongside the SATA data cable from the mobo.
Two more minor issues:
Your power supply might struggle with any more than 2 HDDs. Since you’re just putting in a second, you should be good, but maybe check your PSU to see if you have any headroom. Your manual says you might have a 180W PSU, or a 210W or a 260W. It’s worth taking a look to avoid any future problems.
Are you using TrueNAS to run these drives in RAID? If so, as far as I know, with TrueNAS RAID you can’t mix different HDD sizes in a RAID. Or you can, but it downsizes to the smallest drive size, so you’d effectively have two 8TB drives. If no RAID then I think you’re golden.
UniFi NVR using non-UniFi cameras was a bit tough to set up, at least in a way that has ‘smart’ features. Presumably using UniFi cameras (and/or doorbell) would be much easier. But once running it’s easy to use, and there is a nice “Protect” app. Maybe check a how-to video for the app to take a look, unfortunately there is no demo site from Ubiquiti.