Using full frame lens (FX) on crop frame camera (DX) is safe and fine.
Using crop frame lens (DX) on full frame camera (FX) can work but leaves vignetting around the photos.
Using full frame lens on crop frame camera is kind of like using a big family size suitcase for one person having an overnight stay. You have just clean underwear, spare shirt, pyjamas, and that's all, in a big suitcase with lot of empty spaces around it. So crop frame lens were made to be smaller, just enough to cover the crop frame sensor, in a similar way as having a smaller overnight bag for your few clothes. The idea of having crop frame lenses is to shave off weight, bulk, and costs.
But once you upgrade your crop frame camera (like the D500) for a full frame camera (like the D700), the crop frame lenses will leave your photos with vignetting around the images. So your option is to change your crop frame lenses for full frame lenses.
Normally for a photographer who is happy to stay with a crop frame camera for life, having crop frame lenses does save money, specially if DX lenses are cheaper than FX lenses.
But for a photographer who wants to upgrade from crop camera to full frame camera, it does not justify the costs, as the photographer will have to spend on changing the lenses too.
Thus if a photographer were to already have full frame lenses while using a crop frame camera, and should the photographer decided to upgrade the camera from crop to full, then the photographer will save money because he/she already got full frame lenses for a full frame camera.
You said "I've got the 35mm DX, 50mm and 85mm FX lens. Bought a D700 last year and use a couple of the D series lenses with it."
The D700 is a full frame, therefore the 50mm and 85mm FX lenses are fine with it. But when it comes to the 35mm DX lens, you can use it, but watch out for vignetting around the photos. Your options are, keep the 35mm, but if there are vignetting so use a photo editing software to do what you can with the photo, or change the 35mm DX for a 35mm FX.
If you had a 35mm FX in the first place when you had your D500, and later upgraded to a full frame like the D700, no problem there.