I was wondering if the same captain and first officers always fly together for some time as some sort of a team or are they mixed around in every flight? I suppose if you have one plane that is the case but what happens in huge airlines such as emirates? Wouldn't it also be a drawback always flying with someone that you do not actually know?
In airlines where pilots bid on monthly lines it is conceivable that a pair of pilots fly all month together. However, trip trading and reassignments rarely let this happen. It is far more common that a crew only stays together for a single "pairing" that lasts between 1 and 4 days (domestic 121 USA).
It's not a drawback to fly with new people because training emphasizes standard flying according to the FOM. Ideally, every pilot is exactly the same. Practically it is close enough that you can drop any two pilots from the same airline into an airplane and they more or less operate it exactly the same way.
Do captains and first officers always fly together? No. For large airlines, it would be the exception, rather than norm to fly with the same First Officer several times in a year. For example, consider KLM- it has less 200 aircraft in its fleet, but well over 2000 pilots. Even making allowance for type certification, there are quite a few pilots for each aircraft.
I doubt there would be any drawback in working with a new FO for the first time. Both are fully qualified to fly the plane in all regimes of flight, and usually do so in alternating turns. As an example, the pilots who landed the US Airways Flight 1549 safely in Hudson met for the first time during that flight, though having enormous experience.
Of course, there can be exception to this rule. For example, only 20 pilots were trained to fly the seven Concorde jets of British Airways and as such, they would've flown together more often than others.