I was having the same problems with Aftermarket carbs so I had my original Mikuni totally rebuilt at an ATV Shop for $ 75 including the Complete rebuild Kit! It works great now !!
I always use the Honda oil, and I use 5-30 in the winter, I live in Montana where it gets downright crispy so I like the thinner oil in the cold months
I’ve always stuck with Valvoline ATV Oil. You can get it at Walmart. I’m in NY and it typically gets pretty cold in January. As long as it specific oil for ATVs you should be ok.