hi Pickle!
You have some good ideas, that are not stupid at all. It is my understanding that an authors name, the date, and other metadata can be included in most current picture formats. The system you describe with the serial numbers is very similar to the file hashing system used by Radium SmartChain. Every file, be it a picture, word document, etc produces a unique fingerprint, or hash, which is for all purposes works just like a serial number. It is 100% possible to add hidden data, such as a serial number to a picture, but it may not be necessary when a unique fingerprint/hash can be derived from the file itself. When a file is verified through the SmartChain, the finger print that is unique to that file is forever linked to the username that creates the verification, and the date and time is proven by the date and time of the block in which the transaction exists.
To answer the first part of your question, proof of ownership, ie who made a picture first, is one of the core goals of SmartChain.
The network of nodes that scours the internet for copies, however would be more difficult. Such a system could be circumvented by simply removing the metadata, serial number, etc from the file so that the bots looking for copies would not identify it as a copy. If the bots were to look for a unique finger print instead, the system could be tricked by simply changing one innocuous pixel so that the resulting picture looked exactly the same to a human, but had a different fingerprint. It may be more advantageous to use a google reverse image search, which through some google-magic finds pictures that are similar, but not necessarily exactly the same. A second issue would be that such bots would require a pretty hefty amount of processing power, that I would guess (I didn't actually run any numbers) would make it cost prohibitive.
So in short, it is a great idea, that is pretty much in line with the goals of Radium SmartChain, but I can see some difficulty with implementation. HOWEVER, it does provide the original author with mathematically sound cryptographic proof that they were the original uploaded, which would otherwise be nearly impossible to obtain.
I hope that wasn't too much of an answer
JJ