Many questions

Also, when I add fluid thru the hole by the shifter, does that fill up the entire engine, and transmission? Where else would I need to add?

And how do you tell the temperature of your water or do I not need to worry about it if it is full?

It switches twixt position control to draft control on yur three point hitch.
Use the vertical position when you want a constant height (position control)
Use the horizontal position (draft control) for ground engaging tools -- such as plows.

"Also, when I add fluid thru the hole by the shifter, does that fill up the entire engine, and transmission?"

No -- it just fills the transmission,hydraulics
and rear end. Takes about five gallons. Use 90 WT mineral oil iffn you can find it, or the thinner MC134D, your choice. Most folks here put four anna half gallons inna there so you don't let it get over yur rear axle seals and grease your brakes.

You also need to check your engine oil --
filler in front of your oil filter on the left side of the engine.

As to the radiator: Iffn it has enough water/antifreeze and the thermostat is working and the water pump is working, you should not have to worry about it.
The N tractors did not come from the factory with a temp gauge. You can add one if you want to.

Roger in Michigan