I have an A/V Receiver that has a cable box and blu-ray player running through it via HDMI. I then have a HDMI cable running from the receiver to the TV. Can I put the receiver, cable box and blu-ray in a different box and control all of them through the TV???
Almost all cable boxes come with a universal remote you can program for everything.
Universal remote control would be your best bet. Some tv remote controls allows you to program blu-ray players and cable box too.
Check the remote from your cable company. I have the same signal path you do and my cable company remote allows me to control all those devices and has a basic macro function that allows me to turn them all on or off with a single button. If you need something more sophisticated, check out the Logitech Harmony remotes.
Only through a universal control or if all components support HDMI CEC (Consumer electronic control via HDMI)