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Can two networks be part of the same third octet subnet? If both networks are connected to their own respective links, then could their addresses all be a part of the third octet subnet?

Say a network has a subnet mask of 10.47.80.0/24. Since the network prefix takes up 24 bits, we know that we have 8 bits worth of addresses that can be assigned to end systems connected to the subnet 10.47.80.0/24. Also say that I want to assign 128 [2^7 bits] of the addresses to one network and 128 to another. So basically, I want network #1 (which has 128 possible addresses) to be connected to its own link and network #2 (which has the other possible 128 addresses) to be connected to another link. (Both links, of course, would have a link between them).

Would it be possible to spread out all of the addresses of 10.47.80.0/24 over two networks separated by two links?

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If you are assigned a network, let's pick a valid 10.11.12.0/24 network (not an invalid network, like you have in your question), you can subnet that network into two networks: 10.11.12.0/25 and 10.11.12.128/25. You then assign those two networks, but you do not assign any other networks from your assigned block anywhere else. You cannot assign overlapping networks without a hassle (VRFs, NAT, etc.), and you really need to know what you are doing and have a good reason for doing it.

See the answer to this question for how to do this.

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