Yes, the famous aria in which Figaro introduces himself to Count Almaviva is from Rossini's "Barber of Seville." It's known as "Largo al factotum." Typing those words in Google will get you the Italian lyrics, but I can't find an English singing translation.
There are sound files of bits and pieces of "Marriage" on the web, but it would be an impossible task to put the whole opera together from them. I found
this snatch of Figaro's aria "Non pił andrai" (variously known in English as "Say goodbye now to pastime and play, lad" or "Now your days of philandering are over", which Figaro sings at the end of the first act.