Can't help you out much with the cat issue, all I can say is to tell folks you're not the local dead animal disposal person. For those dead cats that do get put into your trash, leave them there with the trash bin on the street. The eventual stink will give others something to think about. Yeah, I know. The wife and daughter won't agree with that.

How about putting a booby trap (small) explosive on the trash bin lid so that when it's opened, the person gets a real surprise.

Other then that, a security camera directed at your trash bin location will help identify the perpetrators delivering the extra trash and then you can return it to them.

Reference problem number two, all I can do is offer you the chance to exercise that shoulder working at my place.

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Rams
Learning most of life's lessons the hard way. .
You are only young once but, you can be immature indefinitely.