I assume from your description, that others in the building do not have this problem which means that the heat itself is working.
It's possible that when you shutoff the system, the lack of circulation means a pipe could freeze. During the day, it warms up enough to start circulating. This won't necessarily split a pipe, and if it did, it would create other problems. What may be more likely is that there is air trapped in the system, and bleeding it might solve the issue. Are you the highest in the building? It could be that the circulator is 'sticky' and that when it gets shut off, it doesn't want to start running again, but eventually does. Or, you may have a zone valve that is sticky.
If you can't control the temperature well within the unit, and with the other issues, it may be better to address this with the landlord. If you tell him the only way you can cool the unit off is to open the windows in the winter, while keeping things flowing, he may take an interest since it appears you aren't paying for heat directly based on use...it is centralized. If you can talk the landlord into it, they do make some thermostatic water temperature valves for radiators that seem to work well. This would give you room-by-room control of the heating, so you could say keep the bathroom warm, while the bedroom was cooler.