How long should commercial planes stay on the ground after landing before they can take off again? What is the most time-consuming thing/task/operation that happens during this time? Is downloading maintenance data from a plane time-consuming?
Commercial aircraft only make money while in the air, so they should be on the ground as little as possible. How long they are actually on the ground varies with size of aircraft, schedule demands and type of operator.
Transoceanic flights are typically scheduled twice per day for a given aircraft. Schedules are at fixed times and there is usually only enough time for two crossings. This leaves a lot of time to "turn" the aircraft, so the pace is very relaxed.
LCCs on short flight legs try to turn the aircraft as quickly as possible. You have probably heard that when Southwest was just starting out, they were short a plane and had no financing to get another. They reworked their schedule and squeezed a couple more flights out of their existing aircraft to fill the need.
Aircraft manufacturers publish an expected turn time by station. Here is one for a 737-900:
In this example, servicing galleys and boarding passengers tie for longest elapsed time. Refueling is much shorter. Maintenance does not even appear.
More important than elapsed time for any given task is time on the critical path, since many tasks can be done in parallel. In this case, boarding passengers waits for servicing cabin, which waits for deplaning passengers. LCCs typically do not serve meals, so servicing galleys could be significantly shortened. Similarly, they might use a simplified process to shorten boarding time. You might notice that the tasks that have been shortened by LCCs are on the critical path, as you would expect.