Checking whether a site is up or down
A user will probably not be able to hurt your server. You do open your system up to SSRF which might cause a problem, depending on your system. There might also be a possibility to DOS your server as you keep connections open for 60 seconds, which is a rather long time (I'm not quite sure about this, but you should definitely test this). 

You also provide your users the possibility to attack other systems using your server. They may exploit vulnerabilities in other systems that can be exploited via GET, and they may use your server to scan websites because you allow a keyword search. It may also aid in DOS attacks. You may or may not be liable for damages causes by this, I personally wouldn't risk it.

At a minimum, I would disable the keyword search, limit the amount of requests a user can do, and change the user agent to something more honest (eg MyAvailabilityChecker (more info: http://mywebsite.com/availabilitychecker), and provide an option to opt-out).

Regarding your code: It's generally good. A couple of points:


your comments don't add anything (except the comment about time in ms). And they are partly wrong (eg stop after 10 redirects). I would just remove them.
why proc? Shouldn't it be prot? Either way, don't shorten variable names, it makes code harder to read. Same goes for maxredirs. Also, use snake_case for all variables, so it might be max_redirects (max is commonly used, so shortening is ok).
else {$izkey = 0;} is not properly formatted.