Here is an article on Livestrong.com that addresses some of your issues...

What Happens With Too Much Vitamin K?

If you look on the right side of that page there are links to other vitamin K related articles.

From what I read, vitamin K does not thicken or thin the blood. It aids (is required for) blood to clot. Too much vitamin K becomes an issue if you have health problems where a blood thinner is prescribed. Vitamin K can counteract the blood thinning benefit from those drugs, which may increase your risk of clotting.

A vitamin K deficiency can result in slower blood clotting. Some signs of a deficiency include nose bleeds and cuts or other injuries that are slow to stop bleeding. While I was never diagnosed as vitamin K deficient, I have had several occurrences of these symptoms since my teenage years. I've had bouts of spontaneous nose bleeds several times in my life. I've even been to the ER a couple of times for cuts that would not stop bleeding. So I suspect that I have had times where I was vitamin K deficient.

My doctor does have me taking a daily low dose aspirin. At my last annual checkup she ask me for a list of any supplements that I was taking and I did mention that I was taking a K2 supplement. She didn't object.

The Vitamin K2 variation of vitamin K aids in the proper distribution of calcium in the body. That is the main reason I decided to start supplementing. It is supposed to be beneficial for stronger bones and arterial health. So as with many such things, we have to weigh the potential benefits with the risks. I think I get more benefit, so I chose to add K2 to my short list of supplements.