Sorry I don't know if it is made by k&n - Having said that I purchased the screamin' eagle one and that has a k&n stamp on it - on the rubber mounting - have a look on yours - you may find a similar mark? I would not be surprised if yours is made by them as well. I have heard people say that the k&n are the best and they are prepared to pay a **** of a lot more for one in a k&n box but at the end of the day (in my opinion anyway) providing it is a reputable brand it is likely able to do a good job as long as the engine is set up correctly to run with it. I certainly have no complaints about mine - which others have said is $hit !
The oil will make your filter red - I have always assumed it is red so that you can see where you have sprayed it and the colour helps you see if you have missed any areas.
With regard to the material it is made from ? But, having held over a thousand filters in my time I can say that they are either made from gauze, foam or cotton - cotton is the one that this one most resembles so I would be very much surprised if it was anything else.
But whatever air filter oil you are attempting to use should be ok on it providing it is a very 'light' oil. It's like engine / gearbox oil really - the brand is a personal choice.
HD recommends inspecting the filter every 5,000 miles but offers no advice on cleaning or replacing, I don't live in a dusty environment so don't intend to clean mine too often - probably every 25000 miles or so but you are correct in keeping it clean and oiled and it can only go to improve the performance and give you peace of mind that it is a job well done.
The air filter is one of the main components that can have a big impact on how smooth your engine runs - you can go on any forum and find someone complaining that their bike does not run smooth or the idling is rough - others advise all manner of things to improve this (all are probably correct) from draining the fuel tank to clear debris, changing spark plugs / leads etc. etc. but rarely do you see anyone suggest that the air filter may be dirty and once cleaned the bike will likely run a **** of a lot better !