The Growing crystalline structures if you carefully watch the video are forming a protective dome over that city. The city itself if you look very closely isn’t made out of the Crystal material.
The Suns transforming into some kind of structures was shown ages ago in concept art where the Trigs built around the sun a structure to capture it’s energy, other than that I’ve not looked into it further for ages.
The Gallente-empire gate shutting down is a no brainer, the Gate pull power from the local suns, so if you cut that source of energy off by construction of a massive energy trap as noted above, you’d kill all gates in the system, and also turn planets into ice planets, unless a lava planet.
THe Blue Desintegrators is a hard one, with very little time on screen you’d be hard pressed to provide anything more than what was shown.
But the Trig have lived in dark abyssal space since the end of Jove times, and have build tech to allow them to live in dark regions, so capturing suns and turning them into massive powerplants for their planet settlements makes sense.