Fuchsia Dunlop is an author of several excellent Sichuan cookbooks. She trained in Sichuan cooking at the culinary institute in Chengdu. She doesn't do Eastern Chinese cooking to the best of my knowledge. She has just published a revised edition of her excellent cookbook
The Food of Sichuan. I highly recommend it.
Here's a web page that offers a very comprehensive survey of Chinese sauces, etc.:
https://thewoksoflife.com/chinese-sauces-vinegars-oils/. Search this page for "pickled plum".
Regarding bean sauce, there are a bunch of Chinese ingredients that go by that name.
When I see just "bean sauce", I assume that what's meant is a brown, salty paste made from fermented soybeans. It's similar to Japanese miso and you can use dark miso as a substitute. I buy the Koon Chun brand, which comes in glass jars in two versions. The one labeled "Bean Sauce" has whole split fermented soybeans in it. The one labeled "Ground Bean Sauce" is a pureed version that, in my experience, has a milder taste than the one with the intact beans. I usually use the one with the intact beans in it. This is the principal seasoning ingredient in Beijing meat sauce noodles and is also used in Cantonese-style spareribs and roast pork. I think this is the "bean sauce" you saw in your steamed spareribs with plums recipe.
Black bean sauce is made by soaking Chinese black beans (dried, fermented, salted soybeans) in some liquid (rice wine is typical) and mashing them up. Most recipes I've seen call for soaking and mashing the beans yourself, but there are prepared black bean sauces on the market, such as Lee Kim Kee's "Black Bean Garlic Sauce", which also has garlic added. It's a very good time-saving shortcut, like using Lan Chi "Chili Paste with Garlic" when making fish-fragrant (yuxiang) Sichuan dishes.
Doubanjiang or "broad bean paste" is a Sichuan preparation made from fava beans fermented for a year or more with dried red hot chiles. It is a staple in a lot of Sichuan recipes. The best comes from the town of Pixian in Sichuan. Lee Kum Kee's "Chili Bean Sauce" or Toban Djan (non-Sichuan dialect here) is similar, and can be used as a substitute for Pixian doubanjiang, but it has more ingredients and a different taste. It used to be very hard to find Pixian doubanjiang (I finally ran it down at a local oriental supermarket whose proprietor was from Sichuan), but it's now available on the Internet from The Mala Market.
Red bean paste is made by mashing boiled red (adzuki) beans. Sweetened, it's used as a filling in Chinese dessert and dim sum items. It's also sometimes used, as you noted, in making Eastern-Chinese-style spareribs. There are some Sichuan recipes that call for it.
-Paul W.