why amplitude modulation is done for video signals &frequency modulation is done for audio signal in TV?

Answer 1

It is based primarily on historical capabilities and modern compatibility. From Wikipedia:

Modulation
Given all of these parameters, the result is a mostly-continuous analogue signal which can be modulated onto a radio-frequency carrier and transmitted through an antenna. All analogue television systems use vestigial sideband modulation, a form of amplitude modulation in which the lower sideband is incompletely suppressed. This provides a small guard band between the actual video carrier and the bottom frequency in the channel, which helps to reduce interference between transmitters on adjoining channels at a receiver which receives strong signals from both. At the time television was developed, the vestigial sideband was easier to accomplish than true single-sideband modulation; with today's technology, there is no reason for it except to be compatible with existing technology.


[edit] Audio
In analogue television, the sound portion of a broadcast is invariably modulated separately from the video. Most commonly, the audio and video are combined at the transmitter before being presented to the antenna, but in some cases separate aural and visual antennas can be used. In almost all cases, standard wideband frequency modulation is used for the standard monaural audio; the exception is systems used by France, which are AM. Stereo, or more generally multi-channel, audio is encoded using a number of schemes which (except in the French systems) are independent of the video system. The principal systems are NICAM, which uses a digital audio encoding; double-FM (known under a variety of names, notably Zweikanalton, A2 Stereo, West German Stereo, German Stereo or IGR Stereo), in which case each audio channel is separately modulated in FM and added to the broadcast signal; and BTSC (also known as MTS), which multiplexes additional audio channels on the existing FM audio carrier. All three systems are compatible with monaural FM audio, but only NICAM may be used with the French AM audio systems.

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Answer 2

In telecommunications, frequency modulation (FM) conveys information over a carrier wave by varying its frequency (contrast this with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant). In analog applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal. Digital data can be sent by shifting the carrier's frequency among a set of discrete values, a technique known as frequency-shift keying.

Answer 3

probably has something to do with the range of the signal. AM can be sent further then FM.
This can be seen in the angular frequency function.
x(t) = Acos(2(PI)(f)(t))
A is the amplitude
and f is the frequency
Fool around with this and you will see the difference.