That would all depend on context. There's a figure in Irish mythology called the "Red Woman"; you might also be talking about some sort of art or decoration that doesn't use realistic colors (I have a skirt that has a print of little absurdly-colored people on it, so I might say something like, "Darn, I got a stain on my skirt, right there, next to the red woman."); there are some other options that wouldn't be remotely racist.
"rua" is more like red hair, red fur, or I'd imagine also freckled skin--natural reds that appear on people/animals, I think? "dearg" is red in the larger concept, including e.g. red clothes.
It's "bhean" instead of "bean" because feminine nouns are lenited (if possible) after the article.
Adjectives of definite feminine nouns are lenited, too. Generally, when adjectives/genitives get lenited is pretty complex (and I don't have a complete handle on them), so I'm just going to refer you to Gramadach na Gaeilge:
Just trying to understand this (I am Russian) in cross-translation through English to my native language... *sorry for my broken English
We have two words that translate similary in English. It is "рыжий" and "красный". Both will be "red" in English, but the first term is more like natural orange of hair, fur, sometimes to the color of sky or falling leaves, but not to the same-colored objects like, for example, oranges (I mean, fruits) or artifical paints (mean, suspensions, on the wall or smth like that) - in this case it will be "оранжевый" (sounds similary to "orange").
So, if i understood correctly here, in Irish "rua" means same to the russian word "рыжий" but not the "orange" (even if it is same-colored objects)?
rua is used for reddish-brown, russet, rust, copper colours, so gruaig rua is "red hair", madra rua is one of the Irish names for a fox and feamainn rua is "brown seaweed" and bonn rua is a copper coin, capall rua is a chestnut horse (deargrua and donnrua also crop up).
I don't fully understand the distinction between the two Russian words that you describe, but I'm not sure that rua would be an exact match for either of them.
DNTLS doesn't apply to attributive adjectves.
No, I think it just means that somebody at some point thought you should be able to say "pink lady" for the other one and complained that their answer wasn't accepted. I don't know to what extent "bean" overlaps with all the connotations of English "lady," but later in the tree you'll learn "bantiarna," which has the high class/aristocratic meanings of "lady." Personally I'd stick to using "woman" for "bean" to avoid confusion.