I'll take a shot.
R95's muff of a scrimmage kick beyond the neutral zone broke the continuity of downs, but A1's second kick is legal as it occurs behind the neutral zone.
K11 does commit kick catch interference. Even if there were no contact and R80 (seems to be a mix between player R80 and yard line R-20 in the original post) is not blocked going to the ball, K cannot touch a kick in flight if there is an R player in the area (fair catch is irrelevant).
We give an awarded fair catch to R at the R-21, and then add an additional 15 yards for the penalty. R can put the ball in play by a snap or free kick, and can choose which hash mark to put the ball in play on. Clock will start on the snap or first legal touch of the free kick.
Fundamental 1.6 is not violated because K did not legally possess the ball after the KCI penalty. I always ready Fundamental 1.6 to say "no foul IN AND OF ITSELF causes loss of ball". For example - illegal forward pass on 4th down behind the line to gain would mean that the passing team would lose possession of the ball after the foul.
(Edit for completeness: sir55 below is correct that R can also choose to enforce the 15 yard penalty from the previous spot and replay the down - clock starts on the ready. If, for some inexplicable reason, R were to decline the penalty, it would be K's ball, 1st and 10, at the R-19 - clock starts on the snap.).
(Second edit: if R declines the penalty, there is still first touching on the second kick. R's ball, 1st and 10, R-21?)