Should I worry that TimeMachine is making many backups during one night without me using my computer?
It is completely natural for Time Machine to keep backing up when noone is using the computer.

Usually those backups will contains almost no changes, and thus they take up almost no space on the external drive because only changes are backed up. They will eventually push out old backups, but it will probably take a long while because the changes are so small.

Even when not using the computer, there are constantly made small changes to log files, etc. that are transferred over. However note that some virtualisation programs for running Windows, Linux, etc. on the Mac can cause relatively large backups to be made even when almost no user visible changes have been made inside the virtual machine.