Is it safe to enter 'sudo killall mDNSResponder' in Terminal to resolve 'Your computer or network may be sending automated queries' error?

If you want to kill a process, do it in Activity Monitor. That way, you can avoid making a typo in the shell which might cause some unwanted modifications or damage.

Killing any process is generally safe, but it depends…

If the process is running some long-running file modifications/movements/etc, killing it would interrupt that process which may render the files it is working on unusable.

mDNSResponder is not one of those processes and forcing it to quit should be safe.

If you kill a process that runs functions of the GUI, you may have to force shutdown your Mac and restart to recover, losing anything you were working on.

Safe, sure. Effective - probably not. macOS will automatically restart mDNS. Let's flip the question - what are you doing or trying to do that leads to getting this error? What is reporting this error? Is there something beyond receiving the error in and of itself that is not working the way it is expected to work?

In general it's not a good idea to follow Terminal commands you may find posted on the Internet. Start from the beginning and describe the specific circumstances in which you are encountering that error: how / when / where does it appear?

You're off to a good start by using Activity Monitor to identify a process that seems inordinately busy, mDNSResponder in this case, but there can be a variety of reasons for its apparent misbehavior.

In this particular instance that specific command will not result in any harm, so go ahead and try it if you want to experiment. macOS will just reinitiate the process, which is likely to show a lot of activity again.

That has nothing to do with mDNS, at all. On the other hand, are you by any chance using a VPN, or some other "anonyimizer"? That's on of the anti-tracking technologies that Google likes to mess around with on occasion, as are ad blockers and so on.

Is this a Google web-searching "We're sorry, but your computer or network may be sending automated queries. To protect our users, we can't process your request right now."error?

If so, restarting an unrelated part of macOS to resolve what is a questionable or problematic or quite probably incorrect Google error is unlikely to resolve the issue.

Try switching to DuckDuckGo or another of the many fine search engine alternatives available to Google.

I’d suspect that Google tracking is getting tangled and having some difficulty differentiating users, and that difficulty probably due to steps taken to increase user privacy. Other Google mechanisms that I suspect Google is using try to thwart anti-tracking can include repeated displays of captchas, this trying to convince the user to disable their anti-tracking defenses.

Highlight it, click on the tiny x icon.

If it is, read Google Scholar blocks me in Safari. - Apple Community

How do I kill a process in the activity monotor?

There is a Quit button that last I remember is an X inside an octagon.