how to get rid ofhttp://www.apple-security-warning.com

It's a phishing scam. Please ignore it. You can make it go away:

Helpful Links Regarding Malware Problems

If you are having an immediate problem with ads popping up see The Safe Mac » Adware Removal Guide, remove adware that displays pop-up ads and graphics on your Mac, and AdwareMedic. If you require anti-virus protection Thomas Reed recommends using ClamXAV. (Thank you to Thomas Reed for this recommendation.) You might consider adding this Safari extensions: Adblock Plus 1.8.9.

Open Safari, select Preferences from the Safari menu. Click on Extensions icon in the toolbar. Disable all Extensions. If this stops your problem, then re-enable them one by one until the problem returns. Now remove that extension as it is causing the problem.

The following comes from user stevejobsfan0123. I have made minor changes to adapt to this presentation.

Fix Some Browser Pop-ups That Take Over Safari.

Common pop-ups include a message saying the government has seized your computer and you must pay to have it released (often called "Moneypak"), or a phony message saying that your computer has been infected, and you need to call a tech support number (sometimes claiming to be Apple) to get it resolved. First, understand that these pop-ups are not caused by a virus and your computer has not been affected. This "hijack" is limited to your web browser. Also understand that these messages are scams, so do not pay any money, call the listed number, or provide any personal information. This article will outline the solution to dismiss the pop-up.

Quit Safari

Usually, these pop-ups will not go away by either clicking "OK" or "Cancel." Furthermore, several menus in the menu bar may become disabled and show in gray, including the option to quit Safari. You will likely have to force quit Safari. To do this, press Command + option + esc, select Safari, and press Force Quit.

Relaunch Safari

If you relaunch Safari, the page will reopen. To prevent this from happening, hold down the 'Shift' key while opening Safari. This will prevent windows from the last time Safari was running from reopening.

This will not work in all cases. The shift key must be held at the right time, and in some cases, even if done correctly, the window reappears. In these circumstances, after force quitting Safari, turn off Wi-Fi or disconnect Ethernet, depending on how you connect to the Internet. Then relaunch Safari normally. It will try to reload the malicious webpage, but without a connection, it won't be able to. Navigate away from that page by entering a different URL, i.e. www.apple.com, and trying to load it. Now you can reconnect to the Internet, and the page you entered will appear rather than the malicious one.

I am assuming this also applies to the below warning. The thing that makes me nervous is that I actually was unable to even shut down my computer. I finally pulled the plug and restarted... when I did, my desktop went blurry and I got the message "downloading applications." ??? I'm trying to think if there was anything that was supposed to be downloading... I don't think so... 😕 There were some updates available I hadn't selected yet to download, but that is it, as far as I know.

Am I fine--as long as I've gotten rid of this message? Or is there more checking I should do of my Mac?

The best thing to do when a pop-up freezes or locks up your browser is to Force Quit ( --> Force Quit) Safari, then open it Safe Mode by holding down the Shift key. This prevents previous tabs/windows from reopening. Then you can go into your History and remove the site(s) that caused the pop-ups, and it also allows you to go into your Preferences and delete all your cookies and empty your caches.

1. To remove your cookies, go to Safari Preferences --> Privacy and click "Remove all website data"
2. To empty your caches, go to Safari Preferences --> Advanced and make sure "Show Develop menu in menu bar" is checked. Then go up to Develop --> Empty Caches.
3. Check to make sure no extensions were added to your browser without your knowledge. If you see any, uninstall them immediately.

After you do this, you can quit Safari and restart it normally.

Kappy, I very much appreciate your assistance restoring normal function to my Safari browser after a malicious attack by the "***Apple Security Warning***."

Your solution to first, "Force Quit" the Safari application, and then second, to "Hold the Shift Key" while relaunching Safari, was all that was necessary.