I note from your photos the K&N filter was fitted taken directly from the box yet you mention later it can be oiled.
Question 1: Is the filter pre-oil when taken directly from the box?
Question 2: How many kilometres can an oiled filter be used before it needs to be washed and reoiled?
1. Yes, it is preoiled.
2. Follow the factory maintenance guidelines (every 10k miles). For reference, here is the full maintenance interval list: http://hondapcx.org/viewtopic.php?f=15&t=323
Currently ride: Nothing right now - mostly mountain biking with my boys until they're old enough to ride Previously rides: 2011 Honda PCX 125, 2005 V-Strom DL650, 1974 Vespa Ciao, 2011 Honda PCX 170 (tons of mods - takegawa 170cc big bore kit, gears, etc), 1996 Honda Nighthawk 250, 1987 Honda Spree, 2000 KTM 125SX, 2003 Honda Silverwing, 2007 Genuine Buddy 125, 1998 Honda PC800, 2008 Buddy 125 (white), 2008 Buddy 125 (red), 2001 Honda Reflex, 1987 Honda Elite, 1988 Honda Spree, 2007 Yamaha Vino, 2007 Honda Metro, 2x 125cc pure-chinesium dirt bikes