The line that appears over some letters in Hawaiian words is called a kahakō (or macron). Wahine just so happens to be one of the special words that gets a kahakō over one of its vowels when plural. So, wahine -> wāhine. Most words stay the same in spelling whether used in a singular or plural way, but there are a few others that have the same behavior as wahine, such as kaikamahine -> kaikamāhine and makua -> mākua.
This is a good question. Most words don't change in spelling or pronunciation when made plural. It just so happens that wāhine (and some other words like it) are exceptions to the rule. We have already seen wahine -> wāhine. A couple more examples are kaikamahine -> kaikamāhine and makua -> mākua. Definitely check out the Tips & Notes section (the lightbulb button that appears when you click on a skill, on the web only, unfortunately) for more grammar-related info.
Ernest, you wrote (in English) the women, the women. You wrote the same phrase twice. Is that also the answer you gave? This prompt is the womAn (singular), the womEn (plural). The plural needs the line across the A in both "nā" and "wāhine" to be plural. No line over A makes "wahine" singular. Does that help?
The general rule for "ke" is called the "KEAO" rule. Words that start with any of the letters K, E, A, or O are usually led by "ke", and words that start with any other letter are led by "ka". So "ke keiki", "ke keiki kāne", and "ke kaikamahine" fit within that rule.
There are some exceptions though, as Eliza mentioned, for example, "ke poʻo", "ke pākaukau", and "ke ʻeke" (which starts with an ʻokina).
Sometimes there are exceptions to exceptions =) but I wouldn't worry too much about that for now.