Certainly seems like a filter issue. Just slap another filter on there (another A02 even), as they are an excellent filter, and I bet the problem will go away. I run Honda filters on my Honda and have nothing but good things to say about them.
I would change the filter, particularly if this just started at the oil change time. Nothing wrong with an A02 in general but might be something wrong with your particular one.
Our Civic has never done that with any filter.
As for the "oil leak" I would clean it off after the filter change and watch it, suspect that is from the filter change vs a leak. Hard to change the filter without oil running down and along the oil pan rail in both directions.
does this motor have a oil cooler? i would say that oil leak is coming from the filter area. i have had oil filters leak because the rubber seat gets dried out. i bag all my filters up in plastic zip locks now.
My 2001 CR-V w/ ~94k miles has a similar oil light flicker in cold weather. I've encountered this with MaxLife Blend 5w30 using A02 and PureOne filters. The flicker is less pronounced with the P1.