Learn Hardcore Greek: Όταν είμαι κουρασμένος, η συγκέντρωσή μου πέφτει και το εργαστήριο φαίνεται πιο δύσκολο. - When I am tired, my concentration drops and the lab seems more difficult.

In Greek, an adjective like κουρασμένος (tired) normally needs a verb such as είμαι (to be) to form a complete predicate: είμαι κουρασμένος = “I am tired.”
You could also say νιώθω κουρασμένος (“I feel tired”), but that slightly shifts the focus to the feeling rather than the simple state.
Just saying κουρασμένος on its own would sound like a fragment, not a full clause, unless it’s in a very telegraphic style (e.g. notes, messages).

Why is it κουρασμένος and not some other ending, like κουρασμένη or κουρασμένο?

Κουρασμένος agrees in gender, number, and case with the subject (εγώ), which is masculine singular here.
If the speaker were a woman, it would be κουρασμένη; for a mixed or neutral group it could be κουρασμένοι:

Όταν είμαι κουρασμένη… (female speaker)
Όταν είμαστε κουρασμένοι… (we are tired)
So the ending tells you who is tired, grammatically speaking.

Why is it η συγκέντρωσή μου and not το συγκέντρωσή μου?

The noun συγκέντρωση (concentration) is grammatically feminine in Greek, so it takes the feminine article η: η συγκέντρωση.
The possessive μου (“my”) doesn’t change the gender; it just marks possession: η συγκέντρωσή μου = “my concentration.”
So you always match the article to the noun’s grammatical gender, not to the possessor.

Why does the accent move in συγκέντρωση → συγκέντρωσή μου?

On its own, the word is συγκέντρωση (accent on -κέ-).
When you add the enclitic μου, Greek accent rules require the stress to stay within the last three syllables of the whole group συγκέντρωσή μου, so the accent shifts to the last syllable: συγκέντρωσή μου.
This shift happens with many longer words followed by short unstressed pronouns like μου, σου, του.

Why is the possessive μου placed after the noun (η συγκέντρωσή μου) instead of before, like in English?

Greek normally puts possessive pronouns after the noun:

το βιβλίο μου = my book
η συγκέντρωσή μου = my concentration

You don’t say μου συγκέντρωση in standard Greek.
If you want to emphasize the owner strongly, you can use a different structure: η δική μου συγκέντρωση (“my concentration”), but the basic rule is “noun + μου”.

What exactly does πέφτει mean here? Why use a verb that literally means “falls”?

The verb πέφτω literally means “to fall,” but figuratively it also means “to drop, decrease, go down,” just like in English.
So η συγκέντρωσή μου πέφτει is “my concentration drops / goes down.”
You could also say μειώνεται (is reduced) or χειροτερεύει (gets worse), but πέφτει is very natural and colloquial for things like energy, mood, performance, concentration.

Why is it το εργαστήριο φαίνεται πιο δύσκολο and not πιο δύσκολη or πιο δύσκολος?

Εργαστήριο is a neuter noun, so any adjective describing it must also be neuter:

το εργαστήριο → δύσκολο (neuter)
Masculine: δύσκολος, feminine: δύσκολη, neuter: δύσκολο.
Since δύσκολο agrees with το εργαστήριο, the phrase has to be το εργαστήριο φαίνεται πιο δύσκολο.

How does πιο δύσκολο work? Is it the same as saying “more difficult” or “harder”?

Yes. Πιο is the usual way to form the comparative: πιο δύσκολο = “more difficult / harder.”
There is also a synthetic comparative form δυσκολότερο, which is more formal or literary; in everyday speech πιο δύσκολο is much more common.
So both πιο δύσκολο and δυσκολότερο are correct; they mean the same thing here.

Why is the verb φαίνεται used? Does it literally mean “seems/appears” here?

Yes. Φαίνεται is the 3rd person singular of φαίνομαι, and it corresponds to “seems / appears.”
Το εργαστήριο φαίνεται πιο δύσκολο = “the lab seems/appears more difficult (to me).”
Greek doesn’t need to add “to me”; it’s understood from context that it’s your subjective impression.

Why is the verb after όταν in the present tense (είμαι κουρασμένος) instead of something like θα είμαι κουρασμένος?

In Greek, after όταν (when) describing a general or repeated situation, you normally use the present tense:

Όταν είμαι κουρασμένος… = “When I’m tired (whenever that happens)…”

Using θα after όταν is rare and sounds off in this kind of generic statement.
You’d only see future forms with όταν in more specific future-time contexts and often still without θα, e.g. όταν έρθεις, θα μιλήσουμε (“when you come, we’ll talk”). Here the speaker is talking about a general pattern, so the simple present is correct.