What is more convenient, to book a roundtrip ticket with E-dreams or single tickets in their own respective airline websites? For example, if there's a roundtrip flight with Lufthansa and AirFrance, would it be convenient to book the whole ticket with E-dreams or to book the one way flight and the return separately? Would I avoid to pay commission with the latter?
What is more convenient?
It's far more convenient and safer to book with the airlines.
Almost all airlines allow you to book and manage flights on directly on their website. Regardless of what happens it's very clear that the only two parties involved are you and the airline. You will get MUCH better customer service this way, should you need it (Seat reservations, special meals, covid questions, changes, etc.)
E-Dream is a broker that buys tickets on your behalf, which creates a complicated double contract. From their terms and condition:
You will enter into two agreements: (a) one agreement directly with the Travel Supplier(s) relating to the supply of the ordered travel service and (b) one agreement with eDreams relating to the supply of a mediation service.
If you need any services, the airline will not talk to you since you booked through a third party and e-dreams will not talk to you either because their terms & condition states it's not their problem. Let's look at a cancellation and changes
The chance to cancel or change a travel product or service purchased through this Platform, as well as the way to do so, will depend on the terms and conditions of your Travel Supplier(s), which are usually according to the kind of fare chosen (i.e. low cost fares do not usually allow changes or cancellations). eDreams can assist You to find out whether Your fare allows changes or cancellation and, if you wish, eDreams can also manage your request with your Travel Supplier(s), by charging a service fee of FIFTY EUROS (50€) per person and route cancelled and/or changed.
Translation: it's not our problem. If you give us 50 Euros we'll try but there is absolutely no guarantee something will come of it.
So you are stuck in customer service limbo which is very risky especially given the travel unpredictability of the pandemic.
The ONLY reason to book through a 3rd party website is a massive price difference that warrants the additional risk and hassle.
Two one-way tickets are no problem at all. If there is no price difference, I actually prefer two one-ways over a round-trip since it's easier to manage and you have more options if plans change.