Translation:Do you know her?
Actually, I think the two sentences that you wrote must not be what you meant to write, because it is very different. The first is "Do you know her?" and the second is Does she know her?" You must have meant to write 你认识他吗？"Do you know him?" In speaking, with no context it is impossible to know whether "him" or "her" is meant. The problem needs to be reported when it is encounted on the page where the problem is found. There is a repot button on the bottom of the page after you submit an answer.
Rather than thinking of ren4shi 认识 as "know" it may be more beneficial to think of it as "to recognize" or "to be acquainted with" Although English also uses "know" for these ideas, "know" is a bit too general of a term to use as a main gloss, in my opinion, although using it in the translation is often completely acceptable. For example, in English we can say, "I know her", "I know", and "Now I know“, but in Chinese we would say 我认识她，我知道 and 我明白了。More precisely in English we might say, "I'm acquainted with her", "I'm aware (of that)" and "I understand now." 认识一下 ren4shi yi1xia4 is a phrase referring to making an introduction or a first meeting rather than "a little" or "a bit" of a meeting or knowing.
No, you shouldn't. It has been a while since I have done this question...I wish it were easier to report a problem at any time. When you come accross the issue again, try to submit a report that your answer should be accepted. I have done this often, and the moderators have gone in and changed the acceptable answers to include mine. As far as I know, that is the only way to rectify these issues.
You may need other sources of learning. Especially in Mandarin, duo is missing lots of beginner information. If you start to learn the characters, you would recognize the symbol for "woman" at the beginning (I think it might be called a "radical" as it can be combined with many other characters).
Yes, such basic sentences do not hint whether ta1 is masculine or feminine, so we must rely on the character: 她 is feminine; you can see that the left side of the character is 女 , which means woman/female. The masculine pronoun is 他 , the left side of the character is a modified 人 , which means man, or more generally, person. (There is also a neuter pronoun, 它 , also pronounced ta1, used for inanimate objects and animals .) There are various methods one can use to aid in remembering the character for woman, 女 . I imagine it as a woman sitting and cradling a baby in her arms.
It is ren in the fourth tone (starts high and quickly falls). The /r/ in Mandarin is similar to the /z/ in ZsaZsa Gabor, just curl your tongue in and back a bit more. The e is similar to the French e, so overall the sound is much like "je" in French, except that the j is more retroflexed. Then ends with the /n/. :)