Μου αρέσει περισσότερο το γκρι απ' ό,τι το μαύρο.

Because αρέσει works more like is pleasing to.

So:

• μου = to me
• αρέσει = it pleases

That means the sentence is built from the point of view of the thing liked, not the person doing the liking.

A very literal version is:

• Μου αρέσει το γκρι. = Gray pleases me / I like gray

This is one of the first big differences English speakers notice with αρέσει.

A very literal breakdown is:

• Μου = to me
• αρέσει = pleases
• περισσότερο = more
• το γκρι = the gray
• απ' ό,τι = than
• το μαύρο = the black

So the structure is roughly:

To me pleases more the gray than the black.

Natural English, of course, is:

I like gray more than black
or
I prefer gray to black.

Because the grammatical subject is το γκρι, which is singular.

With αρέσει / αρέσουν, the verb agrees with the thing that is pleasing, not with the person.

So:

• Μου αρέσει το γκρι. = I like gray.
• Μου αρέσουν τα χρώματα. = I like the colors.

In your sentence, το μαύρο is part of the comparison, not another subject that makes the verb plural.

Because Greek does not need one here.

The person experiencing the feeling is already shown by μου = to me. So μου already tells us who likes it.

If you want emphasis, you can add:

• Εμένα μου αρέσει περισσότερο το γκρι...

That means something like:

• As for me, I like gray more...
• I personally like gray more...

But in a neutral sentence, leaving out I is completely normal.

Here περισσότερο means more.

It is modifying the idea of liking, so the sentence means:

• I like gray more than black

In other words, it is not saying that gray itself is more in some abstract sense. It is saying your degree of liking is greater.

Yes. That would be very natural.

For example:

• Μου αρέσει πιο πολύ το γκρι απ' ό,τι το μαύρο.

This means the same thing.

Very roughly:

• περισσότερο can sound a little more formal or neutral
• πιο πολύ can sound a little more everyday or conversational

But both are common and correct.

Because the colors are being used as nouns: the color gray, the color black.

So:

• το γκρι = gray / the color gray
• το μαύρο = black / the color black

You can think of an understood noun like χρώμα:

• το γκρι (χρώμα)
• το μαύρο (χρώμα)

Greek often uses the article where English would not.

Here it is functioning as a noun: gray as a color.

But γκρι can also be used adjectivally:

• ένα γκρι πουκάμισο = a gray shirt
• μια γκρι τσάντα = a gray bag

A useful thing to know is that γκρι is generally indeclinable, so it does not change form for gender or number.

By contrast, μαύρο comes from the regular adjective μαύρος, μαύρη, μαύρο. Here it is the neuter singular form, used as a noun:

• το μαύρο = black / the color black

Here απ' ό,τι means than.

It comes from από ό,τι, with από shortened to απ' before a vowel.

So:

• από → απ' before ό,τι

In this sentence, it introduces the second part of the comparison:

• Μου αρέσει περισσότερο το γκρι απ' ό,τι το μαύρο.

You can understand it as a shortened form of:

• Μου αρέσει περισσότερο το γκρι απ' ό,τι (μου αρέσει) το μαύρο.

So the repeated μου αρέσει is left out because it is already understood.

Because ό,τι is different from ότι.

• ότι = that
• ό,τι = whatever / what / than what depending on context

In this sentence, ό,τι is the correct form because it belongs to the comparison structure απ' ό,τι.

Also, the apostrophe in απ' just shows that από has been shortened.

Yes, many speakers would say that, and it is natural.

But the version with απ' ό,τι makes the comparison feel more clearly like:

• I like gray more than I like black

That is, it is really a shortened comparison between two whole ideas:

• I like gray more than I like black

Another very natural way to say the same thing is:

• Προτιμώ το γκρι από το μαύρο. = I prefer gray to black.

Yes. Greek word order is flexible.

Your sentence:

• Μου αρέσει περισσότερο το γκρι απ' ό,τι το μαύρο.

is perfectly natural.

But you could also say:

• Το γκρι μου αρέσει περισσότερο απ' ό,τι το μαύρο.

This puts a little more focus on το γκρι.

In general:

• putting something earlier often gives it more emphasis
• μου usually stays close to the verb

So the meaning stays the same, but the emphasis can shift a little.