Both these tests are with the wheel off the ground.
If you spin a wheel by giving it a quick throw by hand that is a non-dynohub wheel and no brake pads are rubbing, it should go for quite a few seconds before it comes to a stop.
And the way I check a wheel to see if the bearings feel loose is to wrap my hand around a fork blade, I will hold a spoke with index finger and thumb and try to move it sideways, my other fingers are wrapped around the fork blade to hold my hand tight on the fork. If I can feel any perceptible movement, then the bearings are a bit loose. By movement I mean free play between two solid points were it stops, I do not mean simple flexing.
And of course if you heard any noises from the hub that you should not hear, that would be a bad sign.
If it sounds quiet, spins nicely, and has no play, I would be tempted to just quit at this point and keep using it.
If you want to pursue further, see attached file in pdf format, looks like 11 loose balls on each side. It does not say what cone wrench sizes, but I think one is probably 17mm. The other, not sure.
When I have opened up Shimano front hubs for the first time, they always seemed to be pretty stingy with grease.
And usually the first time you open up a Shimano front hub, the cones are so tight you could almost bend a cheaper cone wrench.
A few videos that may help:
Just the first half of this one.
https://www.youtube.com/watch?v=uQJm43eCpWoAnd another.
https://www.youtube.com/watch?v=opommURFB4oAnd I now see Dan found a Park Tool video. So, I will quit looking for a Park one.
I have no clue how far you want to go in trying to figure this out on your own, so I will just quit here. If you get things apart and have no grease or oil to lube the bearings, cooking oil should last until you can get to a good bike shop.
Good luck.