That should be fine, but I would add another NIC so that you can keep the cameras off the internet - plug all the cameras via a switch into one NIC and then the internet into the other NIC
Hmm that might be a problem - the room where the PoE switch plugs into all of the cameras is different to the room where the BI system will be.
You don't have to build a system thought, most of us simply purchase a refurb off of ebay or amazon. A fraction of the cost you will spend to build. And a 4th, 5th, or 6th generation would be more than sufficient.
Not sure if you've seen the rest of the thread, but that's a difficult option because my dad has very specific size constraints - it's a whole thing. At least this way will satisfy that criteria and also build something that will last him for another decade.