It is explained at the site that there is a salvage and recycling ship.
or researching Cylon tech for exploitation and usage
They did, with Starbuck's captured Cylon raider.
researching/teaching Cylon computer code
Very dangerous. Computers need to be primitive and non-networked or the Cylons will take them over. That is the premise for how the Cylons were able to easily destory the human fleet, and only the Galactica (as originally known) got away -- because it was still primitive.
cataloging Cylon strengths/weaknesses vs. humans' for advantages
They have studied and interrogated Cylons. Also, what we see is not necessarily what's going on all over the fleet. You watch a war movie, but you don't always see the cooks and engineers below decks.
BSG and most SF today has sappy, secular-humanist, socialist values prevailing under the most incredible of circumstances
Religion and the value of it is highly placed in the series, and I haven't seen any signs of socialism being promoted. The main socialist in the show is not a good guy.