"She wears underwear."
履く(はく) is the verb for wearing something on your legs or feet, down-up. Trousers, skirts, shoes, socks etc. The polite masu-form of that is はきます.
着る (きる, masu-form きます) is for wearing something around your torso, so these are not interchangable. There are other wearing verbs for covering your head, tying around your neck, or slipping on your fingers/hands (or putting on miscellaneous accessories).
it gets a little confusing; first, the japanese forms we've been learning are not the present tense. -------います means "i do ------" (in general) OR "I will ------"
if you want something being done presently, like i am doing right now, it would be -----ています.
now, as far as the difference, they have different verbs for "wear / put on" depending on where it is. Like skeegenin said:
履きます（は・きます）is i will put on (for below the waist)
着ます（き・ます）is i will put on (for above the waist, such as a shirt, but things on the head have a different verb)
you haven't learned how to say "i am wearing right now" on duo, they haven't shown us those versions.
It is technically called the non-past form, because it is used for both present and future. What you're calling "present tense" is more correctly called "present progressive" in English, which is the "to be —ing" form. The tense corresponding to that in Japanese is the present progressive form using (te-form) + いる.
The present proper is used for sentences like "I wear pants at work" 「会社でズボンを履きます。」
they are in fact the same word. 彼 (か~) means "he" and 女 (~じょ) means "woman/female"
EDIT: wait you meant that somehow かれ + ぬう = かのじょ, didn't you? I can see how that could be confusing if you don't yet know about onyomi and kunyomi readings of kanji. Unfortunately I can't really give any advice beyond researching the onyomi and kunyomi for yourself.
According to my dictionary, パンツ means: underpants, pants, briefs, panties, shorts, knickers
Therefore, using the translation "underwear" here is actually more broad than the word's actual meaning. I have reported this.
As mentioned in another comment, a better word for the more broad term would be 下着 「したぎ」: underwear, undergarment, underclothes, lingerie
I'm not sure if there's a dialectical variation or something, but the English word underwear can mean either any kind of undergarment including bras, or just underpants in particular (see e.g. AHD). In this sentence both of these meanings are plausible without further context. Japanese 下着 seems to be the closest equivalent for the first one, while パンツ suggests the later one. Duo really should accept both when translating from English to Japanese, but I don't know if it does. Another thing is that when translating back from Japanese to English, it's not obvious whether パンツ should be taken to mean underpants or trousers. But generally the translation underwear↔パンツ is reasonable if we assume the sentence talks about underpants.
(Historical aside: I just checked in the Century Dictionary and it described underwear as a trade term for undergarments and marked pants as a colloquial and vulgar way to say pantaloons in one of its meanings.)
を links the object of the phrase with the verb when the object reply to the question "what". Let's try to remove the object for a second. 彼女は履きます->She wears . She wears what? If the object reply to the question what then you need the をparticle. If the object reply to the question where or who, you need the particle に. 彼女は行きます->She goes. Where? 彼女は学校に行きます。 彼女は電話をかけます->She call on the phone. Who? 彼女は友達に電話をかけます。