I can't understand this sentence. It's from a video game Baldur's Gate

I don't speak English well. Please understand my bad grammar. I'm not a native English speaker.

Recently I am playing a video game Baldur's Gate in English.

And I found this from the game.

Dreppin: "Nice day, ain't it? Too bad Nessa here ain't enjoyin' it though, her bein' sick 'n all. I need to get her one of them potions of antidote off Hull."

I understood almost everything what the charater said to me.

But still I don't know why the character used "her being sick and all."

Nessa = female cow

She's sick now. I understand.

But why her being sick? not she is sick or she has been sick or she is being sick.

Why there is no verb in the sentence?
Also how can the character starts the sentence with her, not she?

I mean, we use her usually her ring, her bag as a pronoun. like this. But the character said "her being sick and all."

< it doesn't seem to make sense. Because it's a video game, so just because of that is it ok?

And what does meaning of "and all" ?

her being sick and all. means the female cow is sick now and what?

I don't get what and all means in this sentence.

So please explain the meaning of these things

• meaning of and all
• why her being sick and all / why there is no verb in the sentence
• why her being sick / why the sentence starts with her, not she

Those are my questions. Please help me.

Here is the entry for "and all" in Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013):

and all Also, and all that. Et cetera, and so on; whatever else goes with this statement. For example, We can't afford eating out, since it's hard to find a babysitter, they charge a lot and all, or The contractor will supply the paint and all that. {First half of 1500s}

Ammer's example using "and all" seems rather stilted to me. A more typical U.S. English usage of the idiomatic phrase is this one from Penelope Meriwether, Anatomy of a Life (2013):

I suppose it came down to my mother not being finished sowing her wild oats yet or whatever it is women do. Of course at the time, I had no idea what was going on and if I did, I don't remember, being a baby and all, and consequently, when my father finally tells me about my real mother and why she up and left us and combined with the life I was subjected to because of her not wanting us, as far as I was concerned, I couldn't care less about her ... or so I thought.

And here is a shorter example, from Debra Galant, Rattled: A Novel (2007):

Naturally, she'd volunteered to be a class mom—Connor being new to the school district and all.

Both of these examples resemble the OP's example structurally in taking the form "being X and all." The general sense of the phrase is "being X and all that that entails"—or in other words "being X and having the other characteristics, features, advantages, disadvantages, or whatever else is typically associated with status X."