usually don’t charge you any type of fee so it never hurts
Where Kiwi.com really shines is the way in which it mixes and matches airlines in order to find the cheapest price. For example, maybe you want to go to Rome, Italy from Washington, USA. A typical flight search engine will only suggest routes coming from a single airline and its partners. An example search on Expedia shows the cheapest route as $631.20 USD via TAP Portugal.
Pick a date when nothing is going on and you will get much
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.