Well ! Jerzy never posted over on CMF, so I will post my reply here, in case he comes back, but will keep watching for him to pop up over there as well.
"Real time" or "live" punch-in/punch-out recording is not supported on the Casio CTK/WK-6XXX/7XXX models. The closest you can come is to delete and enter individual events with the Step Editor. See Pages 93 and 94 of the manual.
As for recording Arpeggiator data: The Song Sequencer is actually a 17 track sequencer. "Regular" Tracks 1 thru 16 are referred to as the "B" Tracks and operate as a standard 16 track sequencer, but Track 17, the "System Track", is special in that it operates like a Type 0 MIDI file. It contains 16 additional tracks - the "A" Tracks, which provide for the recording of the Auto-accompaniment rhythm tracks, as well as the associated UPPER-1, UPPER-2 (LAYER), LOWER (SPLIT), Auto-Harmonize, and Arpeggiator tracks. You can not record any of the Auto-accompaniment features "directly" to the "B" Tracks. They record only to the "A" Tracks. The Arpeggiator records to Track-A05. If you need this data on one of the standard "B" tracks you would need to EXTRACT the "A" Tracks to the "B" tracks, bearing in mind that this is a "MOVE" operation that moves data from all "A" tracks and overwrites data on all "B" Tracks with it. Once this is done, you can move the Arp data to which ever "B" Track you need it on. See Page 65 of the manual for the layout of the Song Sequencer tracks. I know this sounds quite involved, but I just recorded 16 bars of the LatinPF arp, did an A-to-B extraction, and used the Track-Edit Copy/Clear commands to move the arp data from Track B05 to Track B01, all in less than two minutes.