I’m worried about my kid’s safety and I want to keep an eye on their whereabouts, I’ve heard that it’s possible to locate a device using its unique identifier, can someone tell me if this method is reliable and if there are any online services that offer this?
Short answer: nope, IMEI tracking is basically a myth for regular people. 
Only carriers and law enforcement can do anything with an IMEI, and even then it’s not a live “here’s where your kid is right now” situation - it’s more of a stolen phone recovery thing.
For actually keeping tabs on your kid’s location, just use Google Family Link (Android) or Screen Time with location sharing (iPhone) - built-in, free, and way more reliable than any sketchy “IMEI tracker” website that’s probably just trying to grab your credit card.