What costs am I actually liable for?

I would expect your liability to be approximately the amount of the vet bills, and the Fair Market Value of the dead sheep, at the time of the...

What can I do to get a company to leave my store alone? They are making false infringement reports against my store.

It sounds to me that you are infringing on the Sun's trademark.

Can I get sued for recreating an already existing online business?

Probably not successfully. . ..

This doesn't appear to fall under the definition of Revenge Porn.

What to do

Cooperate with the police and identify the "lady". Best wishes!

Is this correct and if so would it be OK to apply to a police department in 5 years? What would they think of this?

I don't think that the police department would much care about your close encounter with the snow bank. Go ahead and apply. Intern now if you can.

If I bought a bag of sugar and Crack cocaine was in it can I sue

Funny. No suit. Enjoy.

Can the court/judge interfere/approve in monetary/other settlement between the plaintiff and defendant? or it upto the parties?

Settlement is between the parties.... the judge won't interfere.

Where would I go to learn about buying or renting music licenses so that I would have the ability to stream said music?

BMI or ASCAP or RIAA.

How can I get the IP address from the account so I can show the cops it's her? What do I need to do to get her to stop doing it?

Report the bogus account to FB. They will need your ID.