I would like to ask:
can the coordinator, if he wants, arrange rounds for certain inputs only with this inputs and his own known inputs?
i.e. when the coordinator sees an attempt to register an input of interest to him, he throws out other inputs unknown to him from the round and supplements the round only with his own inputs.
not taking into account how expensive this may be and where the coordinator gets his inputs.
is this technically possible and how can the user be sure that this does not happen?
It's not possible to perform this sort of attack because the user you are targeting may have 2 inputs in the same round. This would allow the target to detect that their second input is suspiciously missing.