You need to take a looks at the TripAdvisor Air Travel forum, where there are many many threads complaining about eDreams and JustFly.
Here is but one example:
https://www.tripadvisor.com/ShowTopic-g1-i10702-k7832000-Edreams_legit-Air_Travel.html
Now put JustFly in the search box and see what comes up.
I have not heard of Exploretrip but you can search them too.
The most common complaint about eDreams is that they lure you in with a low price, you give them your credit card for pay,ent, and several days later they contact you to say the airline has "cancelled your booking" and you need to rebook at a higher price. (Don't do that). Then you have to wIt to get your money back, and you may have trouble getting all of it.
I would not touch any of these third party agents. Expedia is indeed legitimate, but you can have problems with them too. They may advertise a low flight price, but it turns out there is only one ticket at that fare. If you have two,people, you will either have to be on separate tickets, one at each price, or paynthe higher price to get both on one ticket. This happened to a friend of mine.
Another friend, who,lives in Chamonix, bought tickets for his family of four to fly from Milan to,Seattle and back. They drove to Milan Malpensa for the flight and parked their car there. He did not notice until he checked in for the flight home that it landed at Linate, not Malpensa. The itinerary he got from Expedia simply said "Milan" for both flights. I am sure there were actual,airport codes somewhere, but he never saw those. It was a major hassle for his family to transfer between airports after the long trans-Atlantic flight.
Another example, hotel not flights. We were checking in to a nice hotel in Oregon and the family next to us, who had just checked in themselves, asked where to plug in their Tesla. The hotel did not have a Tesla plug-in. They had booked through Expedia, who told them this hotel,did have such a charger. It turns out the charger was at a different hotel,with a similar name ( both names contained the word "river."). The receptionist kindly allowed them to cancel their booking without penalty and re-book at the other place, but I could tell they were stressed out by the mix-up.