Role of Coax Cable in bringing TV signal to our TV sets
"Will the Service provider transmit an AC of radio frequency for all the channel programs into the cable"


Yes, the classic CTV distribution provides all channels simultaneously.


  "which gets converted to EM waves"


No. 


  "and reaches the 3-way splitter?"


Which splitter?


  "Is it just an assumption that the two currents in the coax conductors need to be equal and opposite in order to not radiate outward?"


Yes, that is a weird assumption. There could very well be a DC imbalance between the two currents. The point is that the outer conductor is at ground potential, and encloses the inner conductor.


  "Provided that each channel can occupy only 6-7 MHz band"


which is roughly correct


  "is it obvious that each program produced by the channel will be transmitted at frequencies within this band?"


yes


  "And, if 0-6 MHz is allocated for channel A, 7-12 MHz will be allocated for channel B? To avoid overlapping of frequencies?"


The frequency bands will be non-overlapping, but to match the TV receiver HF part, the frequencies will be choosen to fall into the old over-the-air transmission bands. And there will be some considerable margin between the bands.