Converting a Single-Bulb Light to a Dual-Bulb Light - Your Opinions Please?
Nothing too scary about your situation.  That is fiberglass insulation.  I still would avoid breathing it in.  One thing to start with is that light fixtures do not last forever, especially when they used incandescent bulbs.  They deal with so much heat that the metal parts start to break down.  I recommend that you replace the fixture.  That is a pancake box screwed to the ceiling joist.  Leave it be.  Get rid of everything else except the pancake box and the wires coming through the back of the box.  Purchase a new fixture, preferably with LED lights either integrated of bulb style. Follow the instructions with the new fixture for installation. You can do this! P.