Will 'search' event increment when search result page is not loading or with infinite loops?

@valtsai - Assuming your "search" event fires on load of the results page, and the page loads enough to fire the call to Adobe, then you will see all metrics and dimensions collect and increment in reports. If the page is reloading before the call to Adobe can fire, then you will not see the data collected. You can test this by checking in your preferred debugger or the network tab of your browser's dev tools.

Regarding tracking page load time, I'll point you to the getPageLoadTime() plugin: https://experienceleague.adobe.com/docs/analytics/implementation/vars/plugins/getpageloadtime.html?lang=en 

To track the page load issues/scenarios you mentioned, you'll won't be able to use Analytics. You'll have to find a different service to monitor for issues. For example, if the page doesn't load at all, your Analytics script will not run and no call to Adobe can be made.

If the page does load and fires the event every time on reload, the event will be recorded in Analytics. Recommendation will be to check the code and add fail safe method in the code so that the page does not fall in reload loop. A workaround would be to serialize the event so that Analytics report the event only once.