@fbgluck A network that connects 2 routers would be a transit network. So what IP range to be used would be up to who manages the overall network.
if the downstream network is managed by someone else, and there is no overall person that has access to the complete network, then the owners/admins of the upstream network/router should provide you with the transit IPs to be used. This could be something as small as a /30 or if there might be other routers on the same transit maybe a /29 or /28 even..
But I am kind of with @Jarhead here, maybe it came off the wrong way.. But this does seem like a basic networking 101 sort off question..
As to
1&2) this would be something that does not overlap with the network(s) on the other side of the edge router in your drawing or on the lan side of pfsense. So something other than 10.9/16 or 192.168.0/24, common to use say 172.16/12 rfc1918 block if you are using 10 and 192.168 networks. So an example of this transit network might be 172.16.0.0/30 the upstream is normally the lower IP in the range.. So the edge router would be say .1 and the pfsense wan would be .2 That the upstream be the lower IP is not a written in stone sort of rule, it could be the last IP in the range. But normally its the first IP in the range used for the transit. Also use of small networks for transit is not a rule or anything either, it could be a /24 for example.. You would just want to make sure that the transit networks you use in your network do not overlap with other networks that are routed.
this is pretty clear, on your drawing you show 192.168.0.252, this would be the gateway of devices on the 192.168.0/24 network then.
edit: To your last comment, yeah pfsense doesn't have to nat for sure. Nat would only have to be done upstream in the network where the rfc1918 space might need to get to a public range, etc. Even if you natted at pfsense, you would still need an upstream nat if these devices on your classroom network have need to get off the school network and go to say the internet, etc