Welcome to the forum!
Mid grade gas, or low grade preferably the non ethanol would be best. Definitely not hi grade. That's for performance engines, and it might seem counterintuitive, but it won't help, and will definitely cost a lot more. And might make it not run as good. Non ethanol is a much bigger issue. Lots of people have problems with ethanol. Some areas allow more of it in gas, than others. So if that's your area, you'll want to be especially careful. But most areas have a source for non ethanol. It'll still run just fine with ethanol, lots of people do, and if that's all you have. It's more of a cumulative effect, but it's better not to have it. It seems to gum up the works a bit on some buggies.
Motor oil is determined by outside temperature, and operating practices. So it depends on the season, what area you live, and how you use a given piece of equipment. In the case of a utv, they're not typically driven that hard, so it's more about outside temperatures, in your area.
Thicker oil where I live in semi perpetual summer. Thinner where there's actually seasons. Multi viscosity is how they cover all the bases. It's neither critical, nor rocket science. So unless you're in an extreme environment. Its not a major issue. The lower 48 typically have something around 30wt. Or maybe 40wt. in summer. And usually its a multi weight version. Find out what a similar machine uses. Go with that, keep it changed, when it gets dark.
Can't help you on the gear oil, that would depend on the actual differential. Probably gear oil, but it could be transmission fluid for all I know. These new machines are creatively designed nowadays.
I do know that the seals around ALL the shafts in ANY machine can dry out with lack of use. So when you drive it. Stay close, till you're sure you won't start hemorrhaging fluids. A few drops would be normal for a machine that's sit for awhile. It might clear up after a few drive cycles. As the seals absorb fluid. Or so I'm told. Mine always had to be changed, as they always kept leaking. Good luck!