女

Chinese packs gender right onto the person word with no gap. 女同学, 女老师, 女学生 all read as a single label, like 'saleswoman' in English. Slip a 的 in and the meaning shifts. 女的同学 sounds like 'the classmate of that woman over there'. It makes 女 stand alone as a person, then hands the classmate over to her. People do say 那个女的 for 'that woman', but that's a noun on its own, not a prefix. As a prefix, 女 never takes 的. “六七个男学生，七八个女同学，八九个好朋友。” (Six or seven male students, seven or eight female classmates, eight or nine good friends.) ── [《一两件新衣服》](/read/new-clothes-and-good-friends#s3)

女 can't carry a sentence by itself. To state someone's gender, Chinese adds 的 and turns it into a short label: 她是女的. The same trick builds 男的, 老的, 新的. Drop the 的 and 她是女 sounds like a cut-off news headline. If you'd rather use a plain noun, say 她是女人 or 她是女生. Both are correct, but 她是女的 is what people actually say out loud.

女朋友 is romantic by default. Say 我女朋友 and everyone at the table assumes you two are together. English blurs 'girlfriend' and 'female friend' into one phrase, but Chinese keeps them apart. For a platonic friend who happens to be female, say 我朋友 or 我女生朋友. Mixing this up makes for genuinely awkward dinners. When in doubt, drop the 女 and just say 朋友.