"I know a lot about her."
Translation:Wiem o niej dużo.
I would say, not quite. You wouldn't use "conocer" for knowing a language, would you.
„Znać” is used for things and persons. In Polish, and usually in English as well, the verb is immediately followed by what is known. Like "I know this song" (znam tę piosenkę), "I know you" (znam ciebie), "I know that actor" (znam tamtego aktora), "I know this city" (znam to miasto), "I know English" (znam angielski), "I know the multiplication table" (znam tabliczkę mnożenia).
„Wiedzieć” is more often used for methods and occurrences. These have some connecting words injected, such as „co” or „jak”. For example: "I know how to do it" (wiem jak to zrobić), "I know what happened" (wiem, co się stało).
Sometimes you can rephrase the sentence using one verb with another. For example "I know English" (znam angielski) can become "I know how to speak English" (wiem jak mówić po angielsku). Or this one "I know a lot about her" (wiem o niej dużo) into "I know her well" (znam ją dobrze/dobrze ją znam).
PS: The explanation made with the help of http://www.polszczyzna.fora.pl/kto-pyta-nie-wielbladzi,7/roznica-pomiedzy-znac-i-wiedziec,731.html
You can, but it doesn't mean the same as "I speak English":
Let's see. In this sentence, it just says that you know much about her. You can say that you have many children. That you read a lot of books. Such sentences will use "dużo" (or "bardzo dużo", so 'very many'. They are about the number, the amount of something.
"Bardzo" is generally "very". Sometimes also "very much", but not only. "On jest bardzo silny" (He is very strong), "Bardzo ją kocham" (I love her very much), Bardzo dobrze ją znam (I know her very well.
I hope this explanation, with the examples, is better. Please don't hesitate to ask if something could still use some clarification :)
I'm trying to explain it in another way...
In the sentence "I know a lot about her" the direct object is "a lot", while in "I miss you a lot" we have "you" as a direct object, and "a lot" is used as an adverb.
Technically, "dużo" and "bardzo" are both adverbs, but "dużo" can also be used as a direct object. "Bardzo", like most adverbs, can't take this place in a sentence.
So if you have an English sentence with "a lot" (or "very much"), you should check its function. If it's an adverb, use "bardzo" in Polish. And for the direct object, take "dużo".