Learn Spanish (Latin America): Trabajo durante el día.

Yes, you can! While durante directly translates to "during", you will often hear native speakers use por for periods of the day. For example, saying Trabajo por el día or Trabajo por la mañana (I work in the morning) is completely natural and uses por to show the time period when the action happens.

Why is it el día? Doesn't the -a ending make it feminine?

Día is one of the most common rule-breakers in Spanish! Even though it ends in -a, it is a masculine word. You will always use masculine articles and adjectives with it, like el día (the day) or buenos días (good morning). It is one of those exceptions you just have to memorize.

Why isn't the word yo (I) at the beginning of the sentence?

In Spanish, you can usually drop the subject pronoun (like yo, tú, or nosotros) because the verb ending already tells you who is doing the action. The -o ending on trabajo makes it perfectly clear that "I" am the one working. You would only add yo here if you wanted to emphasize that you work during the day, as opposed to someone else who works at night.