Stream from a windows desktop to multiple TVs/apartments on a separate channel
While what you are asking about is technically possible, it wouldn't be easy or cheap.  It would in fact be very expensive.  To use a channel, you would need to form your own cable network within your house and play different sources for each channel into the system.  These are the kinds of systems that hotels buy to do their own cable network in the building and they can easily cost tens of thousands of dollars.  You would also probably need some pretty expensive licensing from the cable company to rebroadcast their channels so you would need to basically pay for everyone's cable bill.

For the interactive portion (having a stream start when they go to the channel) you actually need a set-top box for each TV as well.  Broadcast networks like cable can only play a signal on a channel to everyone.  They don't normally support starting a video when someone tunes the channel unless the set-top box can communicate back and control the source.  Alternately, the more modern way of approaching it is to have an on-demand type setup where the content isn't streamed in the traditional broadcast manner, but rather is stored on a media server and sent as a digital signal on demand and encoded for a particular set-top box.  This is generally implemented more like Netflix now with a digital stream being sent over a data network allocated to part of the cable network, though some older systems do it as a hidden channel that only that set-top box knows to tune to.

If it is something you still wish to pursue, I suggest looking into manufacturers of different "hotel cable systems" or "private cable systems."  Some quick searching found these guys as one possible option, though I know nothing about them or how good of an option they may be.  They are just the first option I found to give you an idea of what you are looking for.

Update: If you are in a comcast area, it looks like they may also have an option that they can provide to help work it into an actual service agreement which might be cheaper upfront.  See here.