Unlikely, but with them not telling us what's in their additives packages, there's no telling if the additives themselves will do anything when they mix. It's not really advisable to go doing an oil change with 5 quarts of oil from 5 individual brands, for example. If you gotta add oil in an emergency, as long as it's API certified and the right weight, it'll be fine. 

Scotty says pick brand and stick to it. For me, my newer cars I run Pennzoil Platinum in, and my classic, I run Pennzoil High Mileage conventional. I keep quarts for that car in a paper bag on the passenger floorboard when I need to add one. With a car that I know consumes or loses oil, I just buy more than an oil change's worth as a stash and add as necessary.

No. This has been asked here many times. Try entering "oil brand mix" into the search box.

No.