I always wondered if those white vehicles with the UN markings are owned by the United Nations itself, or by various member states?

They are owned by the country providing troops. The UN has no troops nor vehicles of their own (except a few civilian cars/ small trucks for staff personnel), they rely on member nations to provide them.

In addition, the UN reimburses the member states for the use of their troops and vehicles.

Spent a couple of years in the DRC working with MONUSCO out east. Fascinating experience. Yes, contributing nations provide their own gear, weapons, etc. Which makes for this odd mix in country. Quality of troops varies of course. What really makes a difference in operations is how contributing nations communicate to their commanders how they want the UN mandates interpreted. So, some are very aggressive in their patrolling, while others just sit back and won't do anything unless they themselves are directly attacked. The citizens, of course, get very frustrated with the peacekeepers at what the citizens see as a lack of action. You can read all sorts of interesting stuff here....https://monusco.unmissions.org/en/un-reports and pictures here...https://www.flickr.com/photos/monusco/