What is the real difference in lo mein, chow mein, mei fun, and chop suey?

The problem with your question is that you're kind of asking something akin to "what is the universally accepted traditional preparation for Spaghetti". While conventionally in much of the English speaking world, that refers to spaghetti and meat sauce. The word/dish itself refers to a specific style/type of noodle and could be topped with anything.

Lo Mein and Chow Mein refer to the method of preparation and not the contents ("Stirred Noodle" and "Fried Noodle" respectively). They are both often wheat based egg noodles. Lo Mein is typically cooked in a broth, whereas Chow mein, by definition will be cooked in oil. Sometimes it'll be cooked till crispy, sometimes not.

If you happen to be in some location that serves authentic Chinese food, you could order dozens of different preparations for each of the above; It could include various combinations of proteins, vegetables. There are also different types of specific noodles used (eg: the small flat ones usually called "chow mein" in north american restaurants, larger round noodles often referred to as Shanghai Style Chow Mein, etc...). If I walked into a chinese restaurant in Hong Kong and asked for "Chow Mein" in Chinese, I imagine the response would most likely be, "what would you like on it?" Generally speaking there would be some protein and one or more vegetables. This is highly dependent on what is available locally. This varies greatly in China. Hong Kong will have access to more ingredients having been an international westernized port for a long time. The rest of China is more subject to local farming/fishing. That said, Seafood is very common in Hong Kong Cuisine given that it's a port. My friend from the north grew up with a lot more pork. But now my answer is becoming less about the dishes themselves.

Mei Fun means "Rice Noodle". Again, there is no accepted universal rule for what goes into it. My mom who comes from Hong Hong cooks those noodles half a dozen different ways depending on her mood.

Chop Suey like @Ching Chong said, just means "miscellaneous leftovers" or "assorted pieces". The origin is heavily debated and full of myth (see the wiki page). It is most commonly found these days from my understanding in Americanized Chinese restaurants in the US. I don't remember seeing it in Canada for example. Wherever it started, what makes it difficult to answer as it depends on what the cook wants to put in it. Anecdotally, I'm Canadian Chinese and have eaten at Chinese restaurants all over the world since I was born and have never actually ordered this dish, so take my answer for what it's worth. :-)

Lo mein stands for "tossed noodles," and the texture remains soft and it tends to soak up sauces pretty well.

Chow mein stands for "fried noodles," and is either deep fried or stir fried for a longer period of time than lo mein, offering a crisper texture than lo mein.

Mei fun refers to rice noodles, instead of the wheat-based noodles for lo mein or chow mein, so you can get just about any kind of style of dish or flavor, but with noodles made from rice starch (probably good to know for someone with gluten issues).

"Chop Suey" is not authentic traditional Chinese. It's basically a stir-fried hodgepodge of ingredients, so results will vary pretty widely. It actually originated in the USA, but it was created by Chinese immigrants using their cooking techniques on what was handy.

There is no answer to your question. China is a country larger and more varied than the United States. Asking what is "authentic" for something like Mei Fun is like asking what is the "authentic" way to cook chicken, beef stew, or a hot dog. I have eaten in Chinese restaurants all over the world, from California to Maine and from Germany to Chile. Even dishes with the same name vary tremendously depending on what region of China the cook happens to come from.

Their preparation starts with egg noodles made from a mixture of wheat flour and eggs as they proceed to different methods. Chow noodles are either round or flattened. The fresh or dry noodles are boiled to gain softness. The dry noodles are boiled in water for five to six minutes while fresh noodles are boiled for two or three minutes.

These are added to a stir fry mixture and then cooked until they are crispy. Most authentic versions of chow mein in Chinese take-out restaurants have soft noodles.

The difference is due to frying time and amount of oil used. Chow mein results in varied texture within the dish. The other method of preparing chow mein noodles is to fry them separately on a pancake. The stir fry meat and vegetables are then poured on top.

There are two types of chow mein namely; steamed chow mein and crispy chow mein. The steamed version has a softer texture while the other one is crispier and drier. Lo mein preparation starts with fresh noodles only, preferably 0.25 inch thick. They are also boiled and added to a stir fry mixture with a lot of sauce. They are tossed long enough for them to soak the sauce.