To answer the question exactly, I would have to know what kind of lens you have.
In terms of the mount, it definitely fits.
You have an APS-C camera. If the lens is even APS-C, there will be vignetting on a full-frame, or you will crop into the image and lose about half of your pixels.
Theoretically, it could also be that you already have a full-frame lens on your APS-C camera, in which case there would be no problem. So check the lens, then you know the answer.

Yes, you could use your Aps-c lens on the Sony E-mount full-frame camera by switching to Aps-c mode in the menu. However, you will lose half of the resolution.
24mp becomes 12mp.
If you use your Aps-c lens in full frame mode, you will have a large O-shaped vignetting, because the smaller lens cannot cover the whole full frame sensor.