Learn Hardcore Greek: Προσπαθώ να κάνω μικρή αποταμίευση και να αποταμιεύω λίγα χρήματα κάθε μήνα για τις διακοπές μου. - I try to make a small saving and to save a little money every month for my vacation.

κάνω μικρή αποταμίευση = I make a small saving / build up a small amount of savings (as a result).
- This focuses more on the result (“a small saving” as a thing that exists).
- κάνω + noun is a very common Greek pattern: κάνω δίαιτα, κάνω οικονομία, κάνω προσπάθεια.
να αποταμιεύω λίγα χρήματα κάθε μήνα = to be saving a little money every month.
- This focuses on the ongoing, repeated action of putting money aside.

Putting them together is a bit redundant stylistically, but natural: it emphasizes both the general goal (to have some savings) and the concrete way of doing it (saving a bit every month).

What is the difference between να αποταμιεύω and να αποταμιεύσω? Could I say …και να αποταμιεύσω λίγα χρήματα κάθε μήνα?

The difference is aspect:

να αποταμιεύω = imperfective subjunctive → repeated / ongoing action.
- With κάθε μήνα, it fits perfectly: to save some money every month (regularly).
να αποταμιεύσω = perfective subjunctive → one complete action or a one‑off goal.
- More like: to (manage to) save some money (on some occasion / in total).

In your sentence, κάθε μήνα clearly describes a habit, so να αποταμιεύω is the natural choice.
…και να αποταμιεύσω λίγα χρήματα κάθε μήνα sounds odd, because “every month” suggests a repeated process, not a single completed act.

Why do we need να before κάνω and αποταμιεύω after Προσπαθώ?

In Modern Greek, verbs such as:

προσπαθώ (I try)
θέλω (I want)
μπορώ (I can, be able)
πρέπει (must)

are usually followed by να + verb (subjunctive).

So:

Προσπαθώ να κάνω… = I’m trying to do…
Προσπαθώ να αποταμιεύω… = I’m trying to (regularly) save…

Without να, the structure after προσπαθώ would be ungrammatical or would change the meaning completely.

Can we omit the second να and say Προσπαθώ να κάνω μικρή αποταμίευση και αποταμιεύω λίγα χρήματα…?

No, not if you want both verbs to depend on προσπαθώ.

Προσπαθώ να κάνω μικρή αποταμίευση και να αποταμιεύω…
= I’m trying to make a small saving and (trying to) save a little money…

If you drop the second να, the natural reading is:

Προσπαθώ να κάνω… και αποταμιεύω…
= I try to make… and I (actually) save…

So the second part stops being something you “try to do” and becomes a straightforward present statement. To keep the parallel structure (“try to do X and try to do Y”), Greek normally repeats να.

Why is there no article before μικρή αποταμίευση? Why not να κάνω μια μικρή αποταμίευση?

Both are possible, but there is a nuance:

να κάνω μικρή αποταμίευση (no article)
- Sounds a bit more general / abstract: to build up some small level of savings.
- Fits the very common pattern κάνω + bare abstract noun (κάνω δίαιτα, κάνω οικονομία, κάνω υπομονή).
να κάνω μια μικρή αποταμίευση
- Makes it feel more like one specific small saving (one act or one amount).
- Slightly more concrete, as if you had a more defined target in mind.

In everyday speech, both forms would be understood; the sentence as given is very natural.

What gender is αποταμίευση, and how does μικρή agree with it?

Αποταμίευση is feminine.

Nominative singular: η αποταμίευση
Accusative singular: την αποταμίευση

In μικρή αποταμίευση, both words are:

feminine
singular
accusative (because they are the object of κάνω)

So μικρή correctly agrees with αποταμίευση in gender, number, and case.

Why is χρήματα plural, when in English “money” is singular?

In Greek, τα χρήματα is grammatically plural neuter, even though it behaves like an uncountable noun in meaning:

τα χρήματα = money
λίγα χρήματα = a little money / some money
πολλά χρήματα = a lot of money

Greek does have το χρήμα, but:

το χρήμα is more abstract (money as a concept / capital), and much less common in everyday speech.
For normal “I don’t have money”, “I saved money”, etc., Greeks overwhelmingly use τα χρήματα (or τα λεφτά).

So λίγα χρήματα is the natural way to say “a little money” here.

Could we say λίγο χρήμα instead of λίγα χρήματα?

You might occasionally hear λίγο χρήμα in some contexts, but:

The normal, neutral everyday form is λίγα χρήματα or even more commonly λίγα λεφτά.
λίγο χρήμα sounds a bit more like “not much cash / not much money around” in a more stylistic or colloquial way, and it’s less standard in this exact sentence pattern.

So for a learner, it’s safest to stick to:

λίγα χρήματα = a little money
λίγα λεφτά = a little money (more colloquial)

Why is it κάθε μήνα (accusative), not something like κάθε μήνας?

The word κάθε (“every / each”) always takes a singular accusative noun:

κάθε μέρα (every day)
κάθε εβδομάδα (every week)
κάθε χρόνο (every year)
κάθε μήνα (every month)

So κάθε μήνας is incorrect; κάθε does not combine with the nominative in this meaning.

Why are διακοπές in the plural? In English we can also say “my holiday” in the singular.

In Greek:

οι διακοπές (plural) is the normal word for vacation / holidays.
The singular η διακοπή means interruption / cut / break (e.g. διακοπή ρεύματος = power cut), not a holiday.

So for “my holidays / my vacation”, you must use the plural:

οι διακοπές μου = my holiday(s) / my vacation

Even when English uses a singular (“my holiday”), Greek still keeps οι διακοπές in the plural.

Why does μου come after διακοπές (τις διακοπές μου) instead of before, like in English “my holidays”?

Greek uses weak possessive pronouns (μου, σου, του, της, μας, σας, τους) after the noun:

το βιβλίο μου = my book
οι φίλοι σου = your friends
οι διακοπές μου = my holidays

They are clitics, meaning they attach to the noun phrase and don’t carry their own stress.

If you want to emphasize the possessor (“my holidays, not yours”), you can use a strong possessive structure:

οι δικές μου διακοπές = my holidays (with emphasis on “my”)

But the default, unemphasized form is always [article] + noun + weak possessive, as in τις διακοπές μου.

Is για τις διακοπές μου the only option? What’s the difference between για τις διακοπές μου and στις διακοπές μου?

They express different relations:

για τις διακοπές μου = for my holidays (purpose / goal)
- I’m saving this money in order to use it on my holidays.
στις διακοπές μου = during / on my holidays (time / place)
- During my holidays I relax a lot = Στις διακοπές μου ξεκουράζομαι πολύ.

In your sentence, you want the purpose of the saving, so για τις διακοπές μου is the correct prepositional phrase.

Is the word order fixed? Could I say …να αποταμιεύω κάθε μήνα λίγα χρήματα… instead?

Greek word order is fairly flexible, so both are possible:

να αποταμιεύω λίγα χρήματα κάθε μήνα
να αποταμιεύω κάθε μήνα λίγα χρήματα

Both are grammatical and natural. The usual, slightly more common order is:

λίγα χρήματα κάθε μήνα (object first, then time)

Putting κάθε μήνα in the middle (…να αποταμιεύω κάθε μήνα λίγα χρήματα…) adds a tiny bit of emphasis to the regularity (“every month”), but the difference is very small and both versions sound fine.

What tense is Προσπαθώ here, and does it mean “I try” or “I am trying”?

Προσπαθώ is present indicative.

In Modern Greek, the present tense usually covers both:

I try (general habit)
I am trying (right now / ongoing)

Context decides which reading is more natural. With κάθε μήνα (every month), the idea is clearly:

I am (generally) trying / making an effort to save every month.

So it’s like English “I’m trying to save a little money every month.”

Is αποταμιεύω common in spoken Greek, or are there more colloquial alternatives?

Αποταμιεύω is perfectly correct and understood, but it sounds a bit more formal / bookish.

Very common everyday alternatives are:

βάζω λεφτά στην άκρη = to put money aside
- Προσπαθώ να βάζω λίγα λεφτά στην άκρη κάθε μήνα.
μαζεύω λεφτά = to save up money
- Μαζεύω λεφτά για τις διακοπές μου.
κάνω οικονομία = to economize / be frugal
- Προσπαθώ να κάνω οικονομία για τις διακοπές μου.

Your sentence with αποταμιεύω is fine, just a bit more “standard” or careful in tone.