You should solder them onto that terminal you have in that one picture. I do that when installing box terminals so I know chances are it won't come undone like that and for the amplifier should invest in some heat shrink for those power & ground wire connectors and some tape over that as that is just asking for a short or something else to happen.
Also is this the amplifier? If so it "claims" to be 1ohm stable. Also what ohms are the subwoofers? And what ohm do you have them running at? Because that power and ground cable doesn't look all that big maybe 8 gauge? If you could I would run 4 gauge and depending on the rms wattage and ohms you are running them you can decide if you want to go to 1ohm if those subwoofers can handle it and adjust gain from there. Also I personally don't mount amplifiers to boxes because of the vibrations that it can do to amplifier. Some do and have no issues to me I just don't like the look of it since I try to keep the install as clean as possible.
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