Not exactly. Lady is usually pretty formal or super polite in British English, or only used in certain contexts. I wouldn't say "Look at that lady over there, the one drinking the juice", but I might say to a child "Give this to the nice lady, the one drinking the juice".
tamta means that. (when describing a feminine word)
But in Polish "tamta" is more "away" than English "that",
Polish has ta, ta, tamta English has this, that, that.
Because there's no reason to use Instrumental here, the verb "pić", just as most verbs taught at the beginning of the course, takes Accusative.
Well if instead of juice would be tea, then it will change. Ona pije herbatę. The point is that in this case the accusative is not changing.
What kind of juice does "sok" refer to? Only fruit juice, as it is used in these exercises, or any juice?
Well, we don't know. Most likely juice made out of fruits but „sok” can be gathered also from threes e.g birch.
I do have a question. I would say that: "Ja jem pomidora" (it ends with -a because is the complement, WHAT, and its masculine), when I am saying "Ona pije sok", why is not soka? It is because there is some special nowns? Sok is masculine and in this case is a complement so it should be soka, but is not. Thanks in advance!
It's rather the other way round: theoretically it should be "Ja jem pomidor".
"jeść" takes Accusative. Both "pomidor" and "sok" are masculine nouns. Masculine Accusative is the only situation when it matters whether the noun is animate or inanimate. If it's animate, the form looks identical to Genitive. If it's inanimate, the form looks identical to Nominative.
How does this correspond to our situation? Neither juice nor tomato seem to be animate... The problem is, that many nouns are considered grammatically animate without any logic. It is 'technically incorrect', but the vast majority of the population uses it this way. For example I don't think I have ever heard "Jem pomidor" in my entire life, apart from conversations about grammar.
So these weird animate nouns are mostly fruits, vegetables and words connected with new technologies. I would for example add "szampan" (champaigne) here as well. But I cannot imagine any Polish native ever saying "Piję soka". That is definitely not one of those nouns.