It seems the following is occurring: you can navigate any number of websites including Wikipedia and Reuters and everything works OK. Yahoo works OK for a little while, but after navigating a few pages you can no longer do anything with Safari. It does not lock up, but quitting Safari leaves your Mac in a state in which you cannot do anything with it but force it to shut down. Is that correct?
In the first video, Yahoo appears to open with an animated advertisement. At 1:12 in that video, you click on something that is too blurry to identify. It looks vaguely like Google AdChoices. Can you confirm or explain what that is?
After you click on that thing Yahoo no longer seems to function normally. Safari does not exactly freeze, but you can no longer navigate to any other web pages.
To continue troubleshooting, I suggest opening Activity Monitor – it's in your Mac's Utilities folder. Select the CPU tab and sort the % CPU column in descending order (the arrow or chevron should be pointing "down"). In the Window menu, select My Processes. Make the window long enough so that you can see at least a dozen processes.
What you should see will resemble this

Leave Activity Monitor running while you launch Safari and duplicate the problem. When you can no longer navigate Safari, quit Safari, and determine if you can post a screenshot of Activity Monitor (read below). If your Mac's screenshot function does not work when it becomes unresponsive, take a photograph of Activity Monitor and post it in a reply.
Screenshots (Mac):
To take a screenshot hold ⌘ Shift 4 to create a selection crosshair. Click and hold while you drag the crosshair over the area you wish to capture and then release the mouse or trackpad. You will hear a "camera shutter" sound. This will deposit a screenshot named "Screen Shot...." followed by a date and time on your Desktop.
When you post your response, click the "camera" icon above the text field:

This will display a dialog box which enables you to choose the screenshot file (remember it's on your Desktop) and click the Insert Image button. If you are not using full screen mode you can simply drag the image into the text entry field.
⌘ Shift 4 and then pressing the space bar captures the frontmost window.
⌘ Shift 3 captures the entire screen.
Don't capture or upload any information you consider personal. To edit an existing screenshot, read How to edit a screenshot.
Drag the screenshot to the Trash after you post your reply.