Buraya kadar gelmişken sınıfa uğra ve tahtadaki notu fotoğrafla.

Gelmişken is made from gelmiş + -ken.

• gelmiş = has come / came already
• -ken = while / when / since

Together, gelmişken often means something like:

• since you've come
• now that you've come
• while you're here
• since you've come all this way

In everyday Turkish, this structure often introduces a suggestion like while you're at it...

Buraya means to here / here, but buraya kadar adds emphasis:

• buraya = here
• buraya kadar = this far / all the way here

So buraya kadar gelmişken has the feeling of:

• since you've come all the way here
• now that you've come this far

It sounds a bit more persuasive, as if the speaker is saying, You're already here, so you might as well do this too.

Not exactly. It contains a past-like form (gelmiş), but the whole word is not simply a normal past tense sentence.

Here, gelmişken works more like a background clause:

• since you've come
• now that you're here
• while you've already come this far

So it gives the circumstance for the command that follows. It is less about narrating a past event and more about setting up the reason for the request.

Because uğramak meaning to stop by / drop in takes the dative case.

So:

• sınıf = classroom
• sınıfa = to the classroom
• sınıfa uğramak = to stop by the classroom

In the sentence, uğra is the imperative form, so sınıfa uğra means drop by the classroom.

Here it is from uğramak, not uğraşmak.

• uğramak = to stop by, drop in
• uğraşmak = to deal with, struggle with, be busy with

So:

• uğra = imperative of uğramak
• uğraş = imperative of uğraşmak

That is a very common learner confusion.

Tahtadaki is built like this:

• tahta = board
• tahtada = on the board
• tahtadaki = the one on the board / the thing that is on the board

The suffix -ki turns a location phrase into something that can describe a noun.

So:

• tahtadaki not = the note on the board

This is a very common Turkish pattern:

• masadaki kitap = the book on the table
• odadaki öğrenci = the student in the room

Because notu is a definite direct object.

• not = note
• notu = the note as a specific object

In Turkish, specific direct objects usually take the accusative ending. Here the note is specific because it is identified as the note on the board.

So:

• tahtadaki notu fotoğrafla = photograph the note on the board

If you left off the accusative, it would sound less specific, more like photograph a note.

Yes. Fotoğrafla is the imperative of fotoğraflamak, which means to photograph.

So:

• fotoğraflamak = to photograph
• fotoğrafla = photograph it

This is perfectly grammatical. In everyday speech, people also often say things like:

• fotoğrafını çek
• foto çek

Those are more colloquial alternatives, but fotoğrafla is clear and natural.

Because Turkish often leaves out the subject when it is obvious from the verb form or the situation.

This sentence uses informal singular commands, so the subject is understood as you = sen.

So the full idea is:

• (Sen) sınıfa uğra ve tahtadaki notu fotoğrafla.

But saying sen is usually unnecessary unless you want emphasis.

Yes, it is informal singular, used when speaking to one person you are on familiar terms with.

The commands are:

• uğra
• fotoğrafla

A more polite or plural version would be something like:

• Buraya kadar gelmişken sınıfa uğrayın ve tahtadaki notu fotoğraflayın.

In real everyday Turkish, many speakers might also say:

• ... sınıfa uğrayın ve tahtadaki notun fotoğrafını çekin.

That may sound a little more natural in some contexts.

Very often, yes. Not word-for-word, but in many situations the feeling is similar.

In this sentence, gelmişken gives the idea:

• since you're already here
• now that you've come this far
• while you're at it

So the speaker is not just giving two unrelated commands. They are saying that the second action makes sense because the person is already nearby.

No, Turkish word order is flexible, though some versions sound more natural than others.

The given sentence is natural because it flows like this:

1. background circumstance: Buraya kadar gelmişken
2. first command: sınıfa uğra
3. second command: ve tahtadaki notu fotoğrafla

You could move parts around for emphasis, but the original is a very normal conversational order. Turkish often puts the context first and the main action after it, which is exactly what happens here.