To whatever node your client is talking to, the invalid transactions should not be relayed. This is more of a DDOS situation than anything novelly technical. Like all computer systems, DDOS is a technical challenge that requires careful consideration.

Normally there's a fee to try and send such things to prevent such behavior. I haven't seen anything suggesting thats the case for slasher reports.

The thing here is that the validators don't need to be honest when responding to a slasher report.

Do you mean by claiming that the block containing it is invalid when it is valid, or visa versa? Or something else?

Also, how can there be a fee to trying to send an invalid transaction? Such a fee would have to be sent as part of a transaction, yes? Isn’t it just that someone spamming the network gets dropped from the gossip protocol stuff?