There must be some incorrect/missing info in your post as your second question doesn't make sense.
However your front axle rating you will probably never hit as it is just too hard to get that much weight on the front axle. Adding a plow or something like that will get you up there but beyond that you would have a very hard time reaching the front max axle weight.
Rear axle you can certainly hit that with a fifth wheel/gooseneck or heavy load in the bed or wuth a bumper pull trailer if it is really big or you load the heck out of the bed in addition to the trailer.
As far as the truck weighing more than the 10k gvw empty it doesn't. Your scale numbers show that. The axle weight ratings are usually going to be more than the GCW of the truck. Otherwise your load capacity would be very little and or skewed to either the front or the rear. If you cut back the front axle weight rating then you cant put a plow on which while you may not, others do. If you lower the rear axle rating then you have very little load capacity for loads in the bed or towing.
If you went to the scale with the trailer hitched up
front axle= 4460
rear axle= 4280
total gvw= 8740
your vehicle GVWR is 10,000 so good to go, well under the 10k rating as well as both the axle ratings
Your gross combined weight is the 14340 which is surely well below the vehicle GCWR which is probably somewhere up around 20k+
If those scale numbers are without the trailer then you will be hosed on payload capacity as you only have 1260 lbs of available payload left (10000-8740), which seems pretty low for an f250. That leaves 1260 lbs for passengers, other gear, tongue weight of the trailer (lets say 15% of a 6000lb trailer is 900lbs leaving 360 pounds for passengers and other stuff.