I believe it was a civil suit (that's really the only possible way that 80 grand per song couldn't be considered cruel and unusual).

There are statutory damages for infringement of works protected by a federally registered copyright. The reason the statute is written that way is to make trials more efficient, so that once infringement (and registration of the copyright) are proven, the trial court doesn't have to do nit-picky fact-finding about how big the economic damages are from the proven infringement.

Yes. In a recent case, SCOTUS ruled that punitive damages more than 10 times the amount of compensatory (actual) damages is per se unconstitutional except in cases of malice or fraud. Of importance, in followup cases by SCOTUS and the federal appeals courts, the courts have determined that punitive damages in excess of 2x actual damages (or $100,000), which ever is greater, is probably unconstitutional, except in cases of malice or fraud.

When malice or fraud are involved, there is no limit on punitive damages. Note that the fraud must be part of the crime itself; Thomas' perjury on the stand should play no role in punitive damages.

The award will almost certainly be reduced...however...it is likely that Thomas will settle before then. Though $200k was outrageous in the first trial, unique circumstances in this trial make it unlikely that the judge will reduce the amount to anywhere close that number, given that a separate and independent jury found such a large number.