There's no reason your hardware shouldn't be able to run Sims 3 on ultra graphics settings, of course as long as you take the necessary steps to get the same running smoothly. Is your SSD internal? You can and definitely should install Sims 3 on it; loading times will be much faster than if the game were on a mechanical drive or any kind of external drive.
If your external hard drive has a Sims 3 user data folder (saves, mods, saved households, etc.) on it, there's no harm in having it plugged in while installing. And yes, you can transfer over your content once TS3 is up and running. The best practice is to install the game, launch it once to make sure everything is working, then add the content you want to the new folder. Here's a complete list of the subfolders inside the user data folder, including explanations of what each one contains:
https://sims3.crinrict.com/en/2011/01/faq-user-files.html
I can help you get your graphics card recognized, once the game is installed. When you've launched it once and made sure it's working, please go into Documents\Electronic Arts\The Sims 3, open the file labeled deviceconfig.log, copy the lines between "Graphics device info" (about 25 lines down) and "Options" (about 40 lines down), and paste it here.
The other thing you'll need to do, once Sims 3 is running, is manually limit your in-game framerates. This is usually pretty simple, but there's not much point in trying until you can test in-game.
