No. Low pressure compressed air from the inside. Not sure but I think you might be able to wash them gently in soapy water? Best to check on the Apexi website for instructions.
Keep it dry - as Shane said, no oil required, dry-type filter. Avoid water too - low pressure from the inside with air compressor best way to do it.
Not recommended by manufacturer...... not saying it couldn't be done but personally I'd avoid it. And if you do, gentle wash/soak only once, next time replace. Regarding the Apexi Power Intake filters, they say: When the surface is really dirty, when the filter is dry, use a blower to blow air from inside the cleaner to take off the surface dust. Note: Applying water, detergent or oil etc to clean the filter will reduce the filter performance significantly.
I'd recommend Japex Trading - bought one through their eBay store here: Arrived from Japan in a week and genuine article. You can also buy one from CZP in US (not sure if it comes with gasket & bolts or not), item is cheaper but postage is more so about the same cost overall. Could also get one from CJMotor eBay store, more expensive but probably would arrive a few days quicker if really desperate. Be careful you don't get a 'generic' (won't fit) or fake filter just to save a few bucks. Here's a video that shows you some key differences.