No.
DTV sometime needs a better antenna than the old analog TVs. A few stations did not switch to DTV and are still Analog like LPTV which is Low Power TV.
I think you mean a (TV antenna amplifier) RF amplifier used with coax cable. The answer is YES it will work with DTV.
DTV stands for direct TV, an alternative to cable providers. Many people find that DTV is the best option when cable is expensive - or when cable companies prove unreliable or frustrating.
DTV reception is not as forgiving as analog reception was. A better, stronger signal is need in most cases.
As compared to what? Are you talking analog cable or digital cable? Are you comparing it to an analog signal over the air or a satellite receiver?
About the same as VHS compares to DVD.
Yes, certain stations only broadcast in digital bands and can only be seen through a digital tuner. Though these are generally less mainstream programming, but yes they are extra stations.
cross cable
The DTV act making TV stations digital and no more analog channels. Layman's terms: Off air channels, picked up with antenna. "For full-power TV stations, the transition went into effect on Friday June 12, 2009, with stations ending regular programming on their analog signals no later than 11:59 pm local time that day."
Qam
A crossover cable.
Yes, you will need either a Artec or DTV Pal converter box.