To verify that you need to search the exchanger in coinmarket cap. The fake exchanges always have a low capitalization or they aren't even listed on the site. So, that's the right way to know if you can trust on the exchange, and it's important to search for some information about the exchange on this forum, that way if someone get's scammed then they will report it here and give a warning to other users.

And about the coins that don't exist, that's a weird question, you can't buy something that doesn't exist but you can buy something that doesn't have value for other users. So, my advice is; if you want to invest in altcoins then go for the popular ones and avoid tokens and shitcoins.