Yes! Oil can restrict airflow through filters, acting like a choke. Also, oil passing through filters can burn with gas, causing carbon buildup and eventual failure. Oil contacting hot engine can cause partial-combustion fumes, which are dangerous to breathe. I recommend removing oil, and cleaning or replacing filter. Good luck!
Yes, it can. It will suck through your carb(vapors), and burn out your exhaust. Also if the oil is dripping out of your airbox onto a hot engine it will make your eyes burn. But if there is oil in your airbox check your oil level, because that is an indication that it is overfull. It sucks from the crankcase.
Oil on the filter should affect the bike very much since many filters are just oil covered cloth. If the filter is clogged it may make the exhaust smell worse.