No one should try to represent themselves in federal court copyright infringement litigation, it's way too complicated.
If you were going to try to defend yourself, you could appear electronically in the Central District of CA (that's LA), and actual court appearances are rarely if ever required.
If you hired a lawyer, then you'd have to hire a CA lawyer from the LA area or a lawyer who gets admitted "pro hac vice" to the CA Central District court (who can also receive and file documents electronically).
You don't seem surprised that this 2nd claim happened, so you've either maintained a very insecure internet connection or you've been doing some illegal downloading. No one's likely to sue you for $80, but if you expect a lot of these claims to happen, and if the rightsholder is eligible for statutory damages, it becomes worthwhile for the claimant to sue you.
You already paid the 1st $80 claim without getting a release in return, which wasn't smart. Who is this "copyright group"? This may be a scam. Don't do anything else until you consult with an IP litigator.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
This DMCA takedown notice seems highly suspect, and it quite possibly is a scam. DMCA takedown notice are ordinarily provided to a service provider such as You Tube, not to individuals (although if you operate a web site you might receive such a takedown notice). Further, normally there is no economic consequence if an internet service provider (like You Tube) timely complies with the take down notice. Without knowing all of the particular circumstances I cannot be certain if this was a scame, but this is the first I have heard of a company that provides instant justice by providing a link for "settlement."
I would be quite interested in learning more about this alleged "copyright group". I suspect that there are law enforcement officials at both the State and Federal level who would be interested in knowing more about this group.