Η φίλη μου προσφέρει πάντα γλυκό στους καλεσμένους, κι ας είναι κουρασμένη.

In Greek, short possessive words like μου, σου, του often come after the noun:

• η φίλη μου = my friend
• το σπίτι της = her house

This is the normal and most natural position in everyday Greek.
Putting μου before the noun is generally not how possession is expressed in Modern Greek.

Η φίλη μου is in the nominative case because it is the subject of the sentence — the person doing the action.

• η φίλη μου = the subject
• προσφέρει = the verb

So the sentence is built around My friend offers...

Προσφέρει is the 3rd person singular form of προσφέρω.

It matches the subject η φίλη μου, which is she:

• εγώ προσφέρω = I offer
• εσύ προσφέρεις = you offer
• αυτή προσφέρει = she offers

So η φίλη μου προσφέρει means my friend offers.

Here γλυκό means dessert or something sweet. Greek often leaves out the article when talking about something in a general or indefinite way.

So:

• προσφέρει γλυκό = offers dessert / offers something sweet

The singular can sound natural because it refers to dessert as a category or a serving of dessert, not necessarily one single sweet item in a strict counting sense.

Because γλυκό is a neuter noun in Greek when it means dessert.

Greek nouns have grammatical gender, and this does not always match anything logical in English. You simply learn the noun together with its gender:

• το γλυκό = the dessert

So in this sentence, γλυκό is neuter because that is the gender of the noun.

Στους καλεσμένους is the phrase meaning to the guests.

It breaks down like this:

• σε = to
• τους = the
• στους = contracted form of σε τους
• καλεσμένους = guests / invited people

After σε, Greek uses the accusative, so καλεσμένους is masculine plural accusative.

The word καλεσμένος literally means invited or invited person. Very often in Greek, it is used as a noun meaning guest.

So:

• ο καλεσμένος = the guest
• οι καλεσμένοι = the guests

In your sentence, στους καλεσμένους means to the guests.

Κι ας introduces a concessive idea, meaning something like:

• even if
• even though
• although

So:

• κι ας είναι κουρασμένη = even if she is tired / although she is tired

This construction is very common in Greek and often expresses that something happens despite another condition.

Κι is just a shortened form of και.

Before words that begin with a vowel, Greek very often uses κι instead of και, especially in natural speech and writing:

• κι ας instead of και ας

Both relate to and, but in this fixed expression κι ας is the normal form.

In Modern Greek, the subjunctive is usually shown by a particle such as να or ας, not by a completely different verb form in every case.

With είμαι, the form είναι can serve here after ας. So:

• ας είναι = let her be / even if she is

In this sentence, κι ας είναι κουρασμένη is a set concessive pattern, and είναι is exactly what you expect.

Because κουρασμένη agrees with η φίλη, which is feminine singular.

Greek adjectives must agree with the noun they describe in:

• gender
• number
• case

So:

• κουρασμένος = masculine singular
• κουρασμένη = feminine singular
• κουρασμένο = neuter singular

Since friend here is η φίλη, the correct form is κουρασμένη.

Πάντα means always. It modifies the verb προσφέρει.

So:

• προσφέρει πάντα = always offers

Its position here is very natural: after the verb and before the object. Greek word order is flexible, but this placement sounds normal and clear.

Yes. Greek word order is more flexible than English because case endings and verb forms show who is doing what.

For example, you might also hear:

• Η φίλη μου πάντα προσφέρει γλυκό στους καλεσμένους...
• Γλυκό προσφέρει πάντα η φίλη μου...

These versions can change emphasis, but the original sentence is a very natural neutral phrasing.

The comma separates the main statement from the concessive clause:

• main clause: Η φίλη μου προσφέρει πάντα γλυκό στους καλεσμένους
• concessive clause: κι ας είναι κουρασμένη

In English, this works much like a comma before although she is tired or even if she is tired. It helps show that the second part adds a contrasting idea.