In case of telephone broadband, voice signals travels through the telephone line. At the user premise, the modem coverts the voice signals into digital information.
A dialup modem converts between digital signals and analog signals in the voice-band hence why you couldn't use your phone at the same time as your dialup modem..
A DSL modem is generally designed to avoid the voice band. It uses higher frequency signals, filters are used to prevent these high frequency signals reaching the voice equipment allowing voice and DSL to coexist on the same line at the same time.
(1) If the telephone infrastructure is migrated from copper wires to the Fiber Optic cables, then how the data transmission will take place ? Because, the Fiber Optic medium transfers light pulses
Analog voice over fiber is possible in theory but i've never heard of any provider doing it.
If voice is sent over fiber then generaly it will be digitised first. Then the digital data streams will be merged in some way (there are MANY different ways of doing this) and sent down the fiber.
The core of the phone network has been mostly digital for many years. It's much easier to merge, split and switch digital data streams without causing quality problems than it is analog voice signals.
(2) Will I need a different kind of MODEM if I migrate my internet connection from ADSL broadband to Fiber Optic access ?
Terminology varies a bit depending on the exact type of fiber access you are talking about and what exactly you are connecting to it. Devices for GPON seem to be reffered to as "modems", while devices for dedicated fiber tend to be reffered to as "transcivers" or "media converters" but yes you will need a device to convert from the signals used on the long distance fibers and that device will be different from your DSL modem.
(3) In case of Television cable internet, what kind of signals travels through the cable ? And what makes Cable internet faster than ADSL ?
With both DSL and cable the data signals are modulated onto high frequency carriers. The exact modulation schemes are different to suit the different types of cable and to allow coexistance with other services on those cables.
The main reason cable internet is faster is because cable TV cable has better performance (that is it degrades the signals less) at high frequencies than phone pairs do. Phone pairs were designed for analog voice at up to a few kHz and their high frequency performance is pretty poor. Frankly it's amazing that DSL works as well as it does.
On the downside Cable internet has to share the cable with cable TV services which take up a lot more bandwidth than voice does. Cable TV cables are also a shared medium which can lead to congestion problems.