Are “どこに行くの” and “どこに行っているの” both correct? If I regard “ている” in this sentence as “progressive tense”, why is it that I have seen people mostly say 行く? Also, can the ている also be used when talking about habits? For example “彼は毎日3キロ走っている。”
These are two different questions. However, I suppose I'll answer them both.
You have seen 行く because 行っている means something else. The sentence:
Means Father has already arrived at work. In general, ている with movement verbs indicates a completed action.
"Sorry, I'm on my way to school, can I call you later?"
The root verb is 向かう.
As for the ている, it can be used to talk about habits. The sentence you provided looks fine.
EDIT: At the request of OP, I've added some sources, and tried to explain a bit more:
The Dictionary of Basic Japanese Grammar (DBJG), Appendix 2 talks about different Japanese verb types. For the purposes of the ている discussion, let's focus on a few:
Stative Verb: Expresses a state, like ある、飲める, does not usually occur with ている。
Continual Verb: A verb that can be considered an action, and can be done repeatedly. For instance, 作る、書く。ている here expresses the progressive aspect, that is "-ing", as in 食べている.
Punctual Verb: A verb that expresses something that occurs in a single moment, like 忘れる, 死ぬ or 知る. Here 知っている indicates the state after the action was completed, so 知っている means "to know", whereas 知る means something more akin to "acquire the knowledge".
Movement Verb: A verb expressing a movement, like 行く or 来る. It's worth nothing that 歩く and 走る are continual verbs.
Finally, note that some verbs can fit into more than one category. For instance, 分かる can be either stative or continual depending on the context, so for instance 分かっている means something like "I understood before and now understand", which is why it can sound harsher if you're explaining to someone that you understand. Instead, 分かった or 分かる is used.
As for your question about habits, it seems that 走る is also fine. I wasn't sure of the differences myself, but I found this question, I hope it helps you.
DBJG, Appendix 2
DBJG, page 156:
You can also check out this online grammar guide's explanation on page 114, though I prefer the previous resource.