The only time you want to use an amplifier is if you have an extremely long cable run and your experiencing signal loss over it. Another situation might be where you use splitters to feed the same singal to many receievers. Other than those situations you should probably stay away from amplifiers as they themselves will add some noise to the signal. So, if you don't need an amplifier and you still use one anyway, your just going to make your signal quality worse instead of better by adding more noise.
It should work with digital services such as so-called FTA, plus Echostar and DirecTV because the output of the LNBF is analog and NOT digital. The digital signal occurs at the output of the demodulator inside the receiver. However, there are other issues besides signal strength - - the main issue being carrier to noise ratio. Further amplification adds to the noise and reduces the C/N. I would bet the noise factor in that inexpensive amp is rather high.
Since virtually all satellite consumer video services are digital, those pictures are "doctored up". Digital systems have almost no margin between a "perfect picture" and no picture. The best way to improve signal strength (and C/N) is with a larger satellite dish. A LNB with a lower noise factor helps C/N a little too. High quality low loss coax, short coax runs, quality connectors, and minimal connections helps minimize loss of signal strength.
NOTE: A "perfect picture" is defined as how the satellite service provider intended the picture to be received.