Then, it takes me one and a half hours to commute.

If I addinclude commuting time, I spend fifteen hours of a day on the job.

The sentence is fine with 'add'. 'Include' is just an alternative.

Working two days in a row

I have worked two days in a row.

TheMy working hours of my job are fromare 8am to 8pm.

You could say "I work from 8am to 8pm." or "My working hours are 8am to 8pm", or even "My hours are 8am to 8pm"

Then, itIt also takes me one and half hours to commute.

What you write makes sense but this sounds nicer

If I add in commuting time, I spend fifteen hours of a day on the job.

You could also replace "on the job" with "at work"

Working two days in a row

Then, itmy commute takes me one and a half hours to commute.

What you had is also grammatical, but in context, this sounds more natural to me.

If I add my commuting time, I spend fifteen hours of a day on the job.

Or: "the time for my commute"

Because of this, I couldn't sleep much for the last two days, so I'm now too sleepy to write a diary.

The tense didn't make sense to me at first; you should have an adverb or adverbial phrase to make the shift in time clearer. Alternatively, you could write "and I was too sleepy," if you're focusing more on how you felt the last few days than how you feel now.