The 1st waterfall graph basically tells you about the "fidelity" of the speaker. A speaker that keeps moving for long after the signal was terminated is less accurate than a speaker that stops faster. Anyway we are talking about milliseconds, but that is what that graph shows.
The rest are freq response graps, the level at which each frequency is reproduced (actually the level captured by a microphone, since placing the mic at different points will result in different graphs). An Ideal speaker would reproduce all freqs at the same level, so you'd see a flat line. If you search for freq response graphs of reference studio monitors, o very well designed speakers (some designed here at AK), you'll see the response is usually very flat in all the spectrum, moving just some dB up and down (the famous "+- x dB" you read in the specs)
But, all those lines without a text telling what they are, mean basically nothing. Nothing you can read from those graphs. A graph like those needs a text reference, a text telling what thing was measured.
In the last pict, I see a graph with 2 loud peaks near 6KHz and at near 15KHz in a red line, and also a response with those peaks tamed (in green) but with a deep "valley" at 5KHz. Without a text reference, we don't know what those graphs are. Probably the original response, and the "new" response. But it could be another thing too, like measurements from different angles or different heights, or different distance.
Anyway, regarding the "mod", if a speaker has that non linear response, I'd buy a different speaker instead of investing $$ on them. Exception would be if you already listened to the modified version, and they sound that good, better than other speakers you could buy with the same money.
