In Fiber Optic Telephone line, how light signals are converted to the voice signals?
1) Telephone conversations have been digitized within the central office (CO) for decades since electronic switching systems (ESS) starting replacing electromechanical systems like crossbar and step.

This digitizing of the analog signal is done by sampling the voice signal at 8 kHz per second using pulse code modulation (PCM).  It is the same scheme used to digitize audio for compact discs (although the telephone companies sample at a much lower rate -- typically 8 kHz, vs 44.1 kHz for CD's.

The digitizing of telephone links was then extended to long distance trunk lines between CO's.  They use Time Division Multiplexing (TDM) to allow several conversations over one pair of wires.  At first copper lines were still used, then this was replaced by fiber optic inks.

This left only analog lines from the CO to the subscriber's home. Each subscriber line interface did digital to analog conversion. Now copper is being replaced by fiber optic links also, also using TDM.  In addition to time division multiplexing, frequency division multiplexing (FDM)is used to create multiple TDM channels, using different carrier frequencies.

Initially fiber optic was provided to the subscriber's neighborhood, where there would be a cabinet containing the fiber to analog interface to copper pairs going into the subscriber's home.   This is now being upgraded so this interface is located in the subscriber's home, allowing a higher bandwidth connection.  The disadvantage is this interface must now be powered by the subscriber, leaving it vulnerable to power outages.  So this interfaces usually have a battery backup.

2) Yes, you would need different modems.

3) Cable has been historically faster then DSL because it used coaxial cable which has a higher bandwidth than copper.  Cable also uses FDM to share its internet services with television offerings. But with DSL fiber optic direct into the home, this should change.  Cable also has to share its bandwidth among several customers in a neighborhood, so when internet traffic is high, the download speed for each customer suffers.  This is in contrast to DSL, where each customer has a dedicated channel to the CO (whether cable or fiber).  For this reason, cable companies are reluctant to provide static IP's to their customers (which allows the customer to set up servers), while most DSL installations allows this practice.