Newer CPUs will generally idle lower and be more power efficient at low loads and will stay at lower load due to higher processing power. I'd go with the i5-7600.
That said I have my NAS on a Haswell era i5 cpu and it still works well at reasonable wattage. So the T20 would still work.
They still offer free email but you can't use your own domain with it.
I've had a good experience with them. It's pretty much just worked and I never have to think about it. They do have larger plans and ones that have a lot of other services. But their basic email lite plan is $12 a year per mailbox (which can have aliases but not multiple passwords) for 5GB of storage. Or $15 for 10gb.
If you want cheap, I'd go with Zoho. $12 a year per mailbox.
User your router to route between vlans. It will require you set up proper firewall rules. Then you can access it from any system you like.
Alternatively just pass the tagged traffic to your desktop and set them up to each have their own IP address on your main NIC. There really is no reason to have a NIC for each VLAN.
Spectrum will provide a modem only and let you use your own router and AP, but if they won't budge on anything regarding it that's probably not an option.
What exactly are you trying to accomplish though? What will your friends being doing with your NAS? Spectrum doesn't have great upload speeds so at best they'd get slow downloads and at worst it would make your internet unusable with them maxing out the upload.
I don't know why I never thought to just try it out before. Popped in a 10GBaseT module and switched over my mac studio and sure enough, it's running just fine at 10Gb on a cat 5e run.