Also, invalid transactions seem important to understand. I want to know what kind of reprocussions it causes in the ecosystem, if any, or do they just eventually filter into non-existance?
They almost immediately filter into non-existence.
Every node on the network verifies every transaction it receives before it adds the transaction to it's own mempool, or relays the transaction to any other connected peers.
Therefore, if anyone tries to connect to any nodes and broadcast an invalid transaction, every one of those connected peers will reject the invalid transaction. It won't be accepted into their own mempools, AND it won't be relayed to ANY other nodes.
Furthermore, if a node is found to be repeatedly sending invalid data, then the nodes that it is connected to will close that connection so that they don't need to repeatedly check invalid data.