If your flat-panel TV has an analog tuner (which are being phased out), it CAN show static, but modern processing in tuners usually switches the picture to a blue or black screen when the signal to noise ratio of the received station gets too low.
Antenna goes to input, Then output goes to the tv.
Probably nothing, aside from the antenna having an electric charge to it while connected. You might be interested in the wikipedia article on the Tesla Coil.
The antenna.
Yes, if it has an antenna input connector, (RF in).
On its own, it isn't. Amplification requires input of energy - an antenna is entirely passive.
A plasma TV set is just like any other TV set on the market. It can accept video/audio signals from an VHF/UHF antenna if it has an aerial VHF/UHF antenna input. It can also accept DVB-C or DVDB-S or DVB-T through the same antenna input. You have to refer to the manual that came with your plasma TV set to see what types of signals it can receive through its antenna input.
An RF (Radio Frequency) input is the technical term for a coaxial/antenna input on the back of a television. This input is often referred to as simply 'cable' or 'cable vision'.
Maximum transfer of energy occurs when the input Z of the cable and antenna are the same.
If it is widescreen and has an antenna (RF) input.
To decrease antenna height For transmitting a signal of wavelength λ the antenna height must be λ/4. So if we want to send a 1 Hz (λ=3*10^8 m) signal ( very very low frequency) using an antenna , its height must be 75,000 Km ( impossible to build such a huge antenna ). If the same signal is modulated to some high frequency say 88 MHZ ( λ = 3.4 m ) , antenna height needed is 0.8522 m (quite easy to construct !!! ) (88 MHZ is the starting range of Frequency modulation which exists upto 108 MHZ).
It's not uncommon. Look to see if your cable box has an antenna input. If it does, it's just a remote click to change from cable to TV. If not, you'll have to use an antenna switcher.
Try the Winegard HDP-269 High Input Pre-Amplifier 12 dB Digital Antenna.