@silverwood02 Nvidia Inspector is a free download; it doesn't come pre-installed on your computer. It sounds like you're playing in windowed mode, which is why the Control Panel settings aren't working. You can switch to fullscreen on the same options page as your other graphics settings. But even in fullscreen CP sometimes fails to lock in fps, which is why Inspector is so useful.
I doubt you'd damage your graphics card right away with such high frame rates, but you could certainly shorten its life with such a heavy workload. The other consideration is the extra heat generated by the card. Depending on how efficient your computer's cooling apparatus is, you might have a real problem there. Playing for short periods will help, certainly, but fps in the hundreds might be able to overheat a computer in just a few minutes. Again, this is speculation, since I don't know how well your computer handles excess heat. But it's much better to just lock in fps and not have to worry about it.
Edit: I just saw your post on the Sims forums. I play in fullscreen, and I use a resolution of 1280x800. The user interface is big and easy to read, and I can use the highest graphics settings (other than water and high-detail lots, which take extra resources) without taxing my graphics card. For reference, I have an AMD Radeon Pro 560 and a native screen resolution of 2880x1800. Whatever else your settings, if you're going to play in fullscreen, you should make sure that the resolution matches the aspect ratio of your monitor.
Second edit: (because I forgot to mention it) You don't need to run TS3 in compatibility mode. Windows 10 itself is fine.