"They normally go running or hiking on Sundays."
I don't know why this course defaults to "她们" for "they" instead of "他们". It seems to me that "他们" is more likely to be used if the gender of the participants is unknown, because it would apply to a mixed group, but regardless, "他们" should be accepted. Currently it's not.
On a more philosophical note, I don't really understand why there's a "她" at all, since "人" (which becomes the "亻" in "他") is neutral. There's no "ta" made with "男" and "也".
Here's an article that suggests that "她" was an attempt to emulate Western languages in the early 20th century, and "ta" written with Latin letters is a recent attempt to introduce a gender-neutral pronoun back into the language:
This seems ironic, using the Latin alphabet to correct a problem created by emulating Western languages in the first place. Maybe instead a "ta" made with "男" and "也" should be introduced as a masculine pronoun, and then "他" can retake its rightful place as neutral.
Perhaps there are a few, but I'm not at all convinced, particularly without specifics, and considering that there are a number of principles at work in the development of characters. For example, the 人 (亻) radical could be included simply to add the sound element or the "human" element to a sound-meaning compound.
I note that Wikipedia lists about 650 words under the 人 radical. Translating a large number of them with my Zhongwen Chinese Popup Dictionary, I don't see any evidence for your suggestion. There's hardly a "male" character in the bunch. Granted, it might be interesting to survey every single one of them, and see what proportion are indeed "male", and of those, which have 女 counterparts, and when those counterparts came into being.
Did you read the article at the link I posted? It says that "他" was originally used regardless of gender.
Also, "人" is apparently used for the neutral "person" in Japanese, Korean, and Vietnamese (according to Wiktionary), suggesting that it has long been inherently ungendered.
However, whether in the past the default standard person would have widely been considered in these societies to be male would be an interesting question (but a different one).
It either be subject-time or time-subject. I've been done by native speakers that it's just what you want to emphasis (although they've never been too clear to me on which one emphasises what!), but grammatically i think whatever comes first is ultimately the subject of the context for a subsequent clause.