Po pracy oglądam telewizję tylko wtedy, gdy jestem zmęczony.

Because the preposition po requires a specific case here: the locative.

• basic form: praca = work
• after po: po pracy = after work

So po pracy is the correct grammatical form.
A useful thing to remember is that pracy is the locative singular here, even though it happens to look the same as the genitive form.

Because telewizja is the direct object of the verb oglądać = to watch, and direct objects usually take the accusative case.

• nominative: telewizja
• accusative: telewizję

So:

• Oglądam telewizję = I watch TV

In this expression, telewizję usually means television/TV as a medium, not literally just the physical TV set.

Polish often leaves out subject pronouns when they are clear from the verb ending.

• oglądam already means I watch
• jestem already means I am

So ja is not necessary.
You could add it for emphasis:

• Ja oglądam telewizję tylko wtedy, gdy jestem zmęczony.

That would sound more like I watch TV only when I’m tired, possibly contrasting with someone else.

In Polish, the present tense is commonly used for habitual or repeated actions, just like in English.

So oglądam here means something like:

• I watch
• I tend to watch
• I watch as a habit

It does not mean only what is happening right now. It can describe a routine.

Because oglądać is the normal verb for watching TV, films, or other visual content.

• oglądać telewizję = to watch TV
• oglądać film = to watch a film

By contrast, patrzeć means more like to look.

• patrzeć na telewizor = to look at the TV set

So if you mean consuming TV content, oglądać telewizję is the natural choice.

Tylko wtedy, gdy means only when.

It is made of:

• tylko = only
• wtedy = then
• gdy = when

Literally, it is something like only then, when..., but in natural English that becomes only when...

The word wtedy adds emphasis and makes the structure feel very natural and clear in Polish.

You can also sometimes hear:

• tylko gdy jestem zmęczony

That is also understandable, but tylko wtedy, gdy... sounds a bit fuller and more standard.

Both gdy and kiedy can mean when in sentences like this.

So you could also say:

• Po pracy oglądam telewizję tylko wtedy, kiedy jestem zmęczony.

That would mean the same thing.

Very roughly:

• kiedy is very common and neutral in everyday speech
• gdy can sound a little more formal or slightly more written, though it is still completely normal

In this sentence, either one works well.

Because after być = to be, an adjective describing the subject is normally in the nominative.

So:

• jestem zmęczony = I am tired

That is the standard form.

The form zmęczonym is instrumental and would not be the normal choice in this sentence.

Also note that the adjective agrees with the speaker:

• jestem zmęczony if the speaker is male
• jestem zmęczona if the speaker is female

Yes. Polish adjectives agree with the gender of the speaker in this kind of sentence.

So:

• male speaker: jestem zmęczony
• female speaker: jestem zmęczona

Everything else in the sentence stays the same:

• Po pracy oglądam telewizję tylko wtedy, gdy jestem zmęczony.
• Po pracy oglądam telewizję tylko wtedy, gdy jestem zmęczona.

Yes. Polish word order is more flexible than English word order, although different orders can change the emphasis.

The given sentence:

• Po pracy oglądam telewizję tylko wtedy, gdy jestem zmęczony.

is a natural, neutral way to say it.

Other possible orders include:

• Oglądam telewizję po pracy tylko wtedy, gdy jestem zmęczony.
• Tylko wtedy, gdy jestem zmęczony, oglądam telewizję po pracy.

These are grammatical, but the focus shifts a little. The original sentence sounds very natural if you want to start with the time phrase after work.

Usually, yes. In this sentence, po pracy means after finishing work or once work is over.

It is a very common Polish expression. Depending on context, English might translate it as:

• after work
• when I get home from work
• once I’m done with work

But the Polish itself is simply po pracy.