Ό,τι κι αν γίνει τον Ιούνιο, δεν θέλω να ακυρώσω τις διακοπές μου.

These are two different words:

• ότι = that
• ό,τι = whatever / anything that

In your sentence, Ό,τι κι αν γίνει... means whatever happens..., so it must be ό,τι with the comma.

A useful memory trick:

• ότι introduces a statement: Ξέρω ότι έρχεται = I know that he’s coming
• ό,τι means whatever: Πάρε ό,τι θέλεις = Take whatever you want

κι is just a shortened form of και. In this structure, ό,τι κι αν... means something like:

• whatever ...
• no matter what ...

So:

• Ό,τι κι αν γίνει = whatever happens / no matter what happens

This is a very common pattern in Greek:

• όποιος κι αν έρθει = whoever comes
• όπου κι αν πάω = wherever I go
• όταν κι αν γίνει = whenever it happens

So κι αν helps create that indefinite / no matter what meaning.

Because after ό,τι κι αν Greek normally uses the subjunctive, not the indicative.

Here:

• γίνει is the aorist subjunctive form of γίνομαι
• it is triggered by αν in this kind of clause

So:

• Ό,τι κι αν γίνει = whatever may happen / whatever happens

Why not the others?

• γίνεται = present indicative, meaning is happening / happens
• θα γίνει = future, meaning will happen

Greek prefers subjunctive here because the event is uncertain, open, or hypothetical.

γίνει is the 3rd person singular aorist subjunctive of γίνομαι.

Breakdown:

• dictionary form: γίνομαι = to become / to happen
• aorist stem: γίν-
• subjunctive marker in Modern Greek is usually shown by να or by structures with αν
• form here: γίνει = (it) happen

In this sentence, the subject is not stated because Greek often leaves it implied. Here it means whatever happens.

Because τον Ιούνιο is being used as a time expression meaning in June.

In Greek, months are often used with the definite article in the accusative to mean in that month:

• τον Ιανουάριο = in January
• τον Μάιο = in May
• τον Ιούνιο = in June

So Greek often says literally something closer to the June in the accusative, where English uses in June.

Very often, yes, especially in standard everyday usage when talking about time:

• τον Ιούνιο
• τον Αύγουστο
• τον Δεκέμβριο

This is the most natural way to say in June, in August, etc.

You may sometimes see months without an article in other contexts, especially in headings, lists, or less complete phrases, but for ordinary sentences about time, the article is very normal.

Because Greek commonly expresses want to do something with:

• θέλω να + verb

So:

• θέλω να πάω = I want to go
• θέλω να δω = I want to see
• δεν θέλω να ακυρώσω = I don’t want to cancel

This is the standard Greek equivalent of English want to + verb.

Also note:

• δεν negates θέλω
• so the meaning is I do not want to cancel

ακυρώσω is the aorist subjunctive form of ακυρώνω.

After να, Greek uses a subjunctive-type form, and the choice between present and aorist usually depends on aspect:

• να ακυρώνω would suggest an ongoing or repeated action
• να ακυρώσω refers to a single, complete action: to cancel

Since canceling the vacation is seen as one complete act, να ακυρώσω is the natural choice.

In Greek, διακοπές is normally plural when it means vacation / holidays.

So Greek says:

• πάω διακοπές = I’m going on vacation
• οι καλοκαιρινές διακοπές = the summer holidays / vacation
• να ακυρώσω τις διακοπές μου = to cancel my vacation

This is one of those places where Greek and English organize the idea differently:

• English often uses singular: my vacation
• Greek usually uses plural: οι διακοπές μου

Because μου here is a possessive clitic meaning my, and in this kind of noun phrase it normally comes after the noun:

• το βιβλίο μου = my book
• η φίλη μου = my friend
• οι διακοπές μου = my vacation / my holidays

So:

• τις διακοπές μου = my vacation as the direct object

Putting μου before the noun would not be the normal structure for simple possession here.

Because Ό,τι κι αν γίνει τον Ιούνιο is an introductory subordinate clause, and Greek normally separates it with a comma from the main clause:

• Ό,τι κι αν γίνει τον Ιούνιο,
• δεν θέλω να ακυρώσω τις διακοπές μου.

This works much like English:

• Whatever happens in June, I don’t want to cancel my vacation.

Greek word order is more flexible than English, but the given sentence is very natural.

Standard order here:

• subordinate clause first: Ό,τι κι αν γίνει τον Ιούνιο
• main clause after it: δεν θέλω να ακυρώσω τις διακοπές μου

You could change things for emphasis, but not every change sounds equally natural. For example, Greek can move elements around to stress them, but this version is clear and idiomatic.

So for a learner, this is a good model to remember as-is.

Yes. Ό,τι και να γίνει is also very common and means the same thing: whatever happens.

So both are natural:

• Ό,τι κι αν γίνει
• Ό,τι και να γίνει

The version with κι αν is slightly more compact, while και να may feel a bit more straightforward to learners because it clearly shows the familiar να structure. In everyday Greek, both are widely used.