Very nice tractor. And the right previous owner. That series of JD/Yanmars is one of my favorites, and we've had a dozen tractors here.
The hydraulic can't air lock. It's an open hydraulic system and always vented. The air will be swept out by the moving fluid in a matter of minutes at most. You probably won't even notice. Working the loader will help that, but again I doubt that you will know.
Check and see if you also have a cleanable screen type hydraulic filter on the side of the transmission (sump). I believe that yours did. That will definitely need a cleaning at 1000 hours. The additional hydraulic spin-on filter is like any other. Use a genuine spin-on, it is heavier built for a reason.
On the hydraulic fluid, if you got JD Hy-Gard trans/hydraulic oil you are good to go. BTW, DO NOT use hydraulic oil. Hydraulic fluid will ruin it. What you want is dual purpose transmission/hydraulic fluid. Your transmission and hydraulics share a common sump.
That dual use fluid is much more expensive; it has to be thin enough to be hydraulic fluid but have the shear strength of a gear oil. That magic is done with additives - which is why it is so much more expensive. This isn't some sort of conspiracy; good trans/hydraulic oil will go a thousand hours but it is costly. The JD Hy-Gard is a proprietary formula - as are all the trans/hydraulic oils. There are no lubrication or additive standards for trans/hydraulic oils, so there is no way an after market oil can meet a spec that doesn't even exist. The JD Hy-Gard has the specific additives for the internals of your transmission & hydraulics. It isn't the only good oil on the market, but the all cost about the same. Part of that cost is in the additives. The high dollar oils have an additive formulation that protects brass and bronze alloy bushings, Look it up if you are curious. There are other good transmission/hydraulic oils. I'm not pushing JD products, if you know what you are looking for, Chevron makes one and so does New Holland, Caterpillar, Kubota sells one that they don't make, and there are lots of others. But they all cost about the same.
You have found a tractor that should last a lifetime. If you would rather use aftermarket oil to save a few bucks I'd stop and question the whole project. Maybe just change the filters and call it good. There's a way to do that which kinda works. Why gamble?
rScotty