Learn Spanish (Latin America): ¿No vienes? Pues voy solo. - You're not coming? Well then, I'll go alone.

Yes! While por eso means "that's why" or "therefore," pues is a very common filler word that translates to "well" or "well then." Here, it connects the consequence (voy solo) to the situation (¿No vienes?). You could say "No vienes, por eso voy solo" (You aren't coming, that's why I'm going alone), but using pues makes for a very natural, casual response.

Why does the translation say "I'll go" when voy is in the present tense?

In Spanish, the present tense is frequently used to talk about the near future or immediate decisions. Saying voy (I go / I am going) is much more common in everyday spoken Spanish for an action you just decided to take right now, rather than using a strict future tense.

If a woman were saying this sentence, would she still use solo?

No, she would say sola. In this sentence, solo is an adjective meaning "alone," so its ending must match the gender of the person it describes. This is different from the adverb solo (meaning "only"), which never changes its ending.

Is it important to use vienes (you come) in the first half and voy (I go) in the second half?