How do I resolve 'Ads.fiancetrack(2).dll' infection and Safari freezing when opening Google email links on Mac?

Just use Malwarebytes (free version) if you have any reason to suspect. Also, please read KiltedTim's post, he is correct.

Finally, if it's an unwanted popup then please read and follow the troubleshooting steps in Block pop-up ads and windows in Safari - Apple Support

Please download and run malwarebytes and if you installed any adware or malware then malwarebytes will remove it.

A few things to add to what the others have provided you:

• A file, ending in "dll," is not something that can run under macOS. These are typically associated with the Windows operating system. That's one clue that this is a scam.
• Look at the URL listed in the Google Chrome's address bar, ending in "web.core.windows.net." This scam was, most likely, aimed at Windows users and get them to respond to the pop's "Scan" button. Doing so, could infect a Windows device. Regardless, you did the right thing by not selecting it.
• Apple NEVER sends you a security alert. The fake "Apple Security Center" title of the pop-up window is to fool you other wise. If you are in doubt when you see these, you can contact Apple Support directly, and/or, post here so that other Apple-product users can assist you.
• Finally, I strongly suggest that you stop using Google Chrome. Better still stop using Google apps all together. If you don't like using Safari, and prefer the Chrome-like look, I suggest that you try Brave. Others here will also suggest FireFox.

That is a popup ad scam. You are not infected.

Do NOT use any contact links or phone numbers in that message. It did NOT come from Apple.

Your screenshot indicates the "Malwarebytes" product was already installed. Since it apparently failed to prevent that scam message from appearing, I suggest you uninstall it.

The decision to keep it installed or not is yours. It may not be doing any harm, but in my opinion if something is not providing a benefit then it's not worth keeping installed. Should you ever find yourself deceived into installing something actually harmful, removing whatever it may be is easily accomplished without having to install yet something else.

Read Phony "tech support" / "ransomware" popups and web pages - Apple Community for a few more examples of these common scams. They are not viruses, and they are not malware. They're just images, pictures, inert and utterly harmless in and of themselves. The information they portray is just a pathetic lie. A picture cannot harm anything. Problems only arise when people choose to believe what they say.

Please be circumspect when choosing to upload screenshots to this site or any other publicly viewable website. The screenshot you posted reveals some personal information — a piece of a calendar, a house plan website, your local currency symbol... that sort of thing. Sometimes even the lack of information can be a clue, if a website such as Apple's is missing some information present elsewhere. That's the kind of information scam artists with a lot of time on their hands exploit to defraud people.

The information you posted is probably not enough to warrant concern or to ask the site Hosts to remove, but it is more information than required to address the problem at hand.