ביום שישי אני בחופש, אבל הוא דווקא עובד עד הצהריים.

Because Hebrew usually attaches certain one-letter prepositions directly to the next word.

• ב־ = in / on / at
• יום = day

So:

• ב + יום = ביום

In this sentence, ביום שישי means on Friday.

In Hebrew, the days of the week are often named by number.

• יום ראשון = Sunday, literally first day
• יום שני = Monday, literally second day
• ...
• יום שישי = Friday, literally sixth day

So שישי means sixth, and with יום it becomes Friday.

Hebrew normally does not use the verb to be in the present tense.

So:

• אני בחופש = I am on vacation / I’m off
• literally: I on vacation

This is completely normal Hebrew.
If you wanted past or future, then Hebrew would use forms of להיות:

• הייתי בחופש = I was on vacation
• אהיה בחופש = I will be on vacation

בחופש is made of:

• ב־ = in / on
• חופש = vacation, break, time off, freedom

In this sentence, אני בחופש is an idiomatic way to say:

• I’m off
• I’m on vacation
• I’m on break / not working

It does not mean I am free in the general adjective sense.
For free as an adjective, Hebrew often uses חופשי.

So:

• אני בחופש = I’m off / on vacation
• אני חופשי = I’m free

דווקא is a very common Hebrew word with several shades of meaning. Here it adds a sense of contrast, unexpectedness, or emphasis.

In this sentence:

• אבל הוא דווקא עובד = but he actually / in fact / דווקא is working

A natural English sense would be something like:

• but he, on the other hand, is actually working
• but he’s דווקא working
• but he’s the one who is working

So דווקא makes the contrast stronger than plain אבל by itself.

Because עובד is the masculine singular present-tense form, and it agrees with הוא (he).

• הוא עובד = he works / he is working
• היא עובדת = she works / she is working

Hebrew present tense often works like both English simple present and present continuous, so הוא עובד can mean either:

• he works
• he is working

The exact meaning depends on context.

עד means until / up to.

הצהריים refers to midday / noon / the early afternoon period, depending on context.

So עד הצהריים can mean:

• until noon
• until midday
• sometimes until the early afternoon

The exact English translation depends on the situation, but the core idea is that he works up to around midday.

The ה־ is the definite article, like the in English.

Hebrew often uses the article with parts of the day:

• בבוקר = in the morning
• בערב = in the evening
• בצהריים / בצהריים and הצהריים are also common time expressions

So עד הצהריים is naturally understood as until the noon / until midday, which in English we simply say as until noon or until the afternoon depending on context.

Hebrew word order is fairly flexible. Putting ביום שישי first sets the time frame right away:

• ביום שישי אני בחופש = On Friday, I’m off

This is very natural Hebrew. You could also say:

• אני בחופש ביום שישי

but starting with the time phrase often sounds smoother when you want to establish the setting first.

Yes, אבל already means but, so it introduces contrast by itself.

However, דווקא adds an extra layer:

• אבל הוא עובד = but he works
• אבל הוא דווקא עובד = but he actually / specifically is working

So together they mean something like:

• I’m off on Friday, but he, interestingly enough, is actually working until noon

It makes the contrast feel more pointed or slightly surprising.