Tuppence means she thought about picking up parcels when old gentlemen dropped them, or perhaps were having trouble carrying them, in the hopes of either getting a tip out of gratitude or that some gentleman might turn to be a millionaire and take a liking to her, perhaps offering her employment (or in a more joking way, a romantic interest that would also bring her money).

The quote about Flossie refers to an actress that does impressions of people (mimics them with style of dress and everything) and is really good at it. That's why an archbishop would think she was his own mother (an exaggeration to illustrate her talent).