A schedule is a plan which indicates a time or sequence. "We're on schedule" means that we are where and when we have previously planned to be, and that we are currently following the plan/schedule. If the schedule is "short on time", then we could also be "short on time", despite being "on schedule". However, this is very rare, since most people do not plan a schedule which is "short on time". One reason you normally plan a schedule at all is so that you will not be "short on time".

It means that things have to be done within a certain timef rame/timetable

I think no, we do not have to limit the time, it's just for formal

No I think it means we have to respect the deadline