If you're flying somewhere that involves a transfer, say from Canada to Australia which typically involves Canada to LA, then LA to Australia, consider that it may be cheaper to book these two legs separately on your own by adding another destination to your trip. It should go without saying that in doing this, you should not book tight layovers. I repeat: do not book layovers that are hours apart! This approach is for those who want to create an additional destination of a few days or more, before catching their next flight. The one exception is when booking with Kiwi.com, who offer their own guarantee on making connecting flights even when not with the same partner airlines.
You're not crazy for thinking that a flight price has changed after searching it a few times in your web browser. Based on the cookies in your browser, flight prices do increase when a particular route is repeatedly searched, as the site wants to scare you into booking the flight quickly before prices get even higher. Always search for flights in incognito or private browsing mode to see the lowest prices.