Really, really good question. Close to a real one.
1) The LSST must come first, as close as the beginning of the sentence.
2) The right tense after that
3) The rest of the sentence
This is step by step the process that a student should follow when a difficult question raises the bar. You need to push and push more on the nuances in the sentences.
Scan them always vertically, this is quite importantThe red parts = wrong
The blue parts = right
(A) The LSST, designed to study the evolution of the universe, can capture most of the changes occurring in the sky
as established in the quality of its images and
by the huge area covered by it per second as well as
Two problems here: as because there we should have a verbe and by is not parallel
(B)
Establishing that the LSST, which was designed to study the evolution of the universe, will capture most of the changes occurring in the sky are the quality of its images and the huge area covered by it per second, and also the
wrong the placement at the beginning of the sentence
(C) That the LSST, designed to study the evolution of the universe, can capture most of the changes occurring in the sky
is established
by the quality of its images and the huge area covered
by it per second, as well as by the
look nice
(D) The LSST, which has been designed to study the evolution of the universe,
captures most of the changes occurring in the sky,
as establishes the quality of its images and the huge area covered
by it per second, as well as the
sound like the LSST captures on its own something and NOT as a piece of machinery is able to do something
(E) The LSST, designed to study the evolution of the universe,
probably will be able to capture most of the changes occurring in the sky,
was established by the quality of its images, the huge area covered by it per second, and the
C is the best answer