Çay için teşekkürler.

İçin usually means for. In Çay için teşekkürler, it links çay and teşekkürler to give the idea thanks for the tea.

So the pattern is:

• X için teşekkürler = thanks for X

Examples:

• Yardım için teşekkürler. = Thanks for the help.
• Davet için teşekkürler. = Thanks for the invitation.

Both are possible, but they feel a little different.

• Teşekkürler = thanks
• Teşekkür ederim = I thank you / thank you

Teşekkürler is shorter and a bit more casual or conversational. Teşekkür ederim is more complete and often sounds a little more polite or formal.

So:

• Çay için teşekkürler. = natural, short, everyday
• Çay için teşekkür ederim. = also natural, slightly more formal/polite

Because çay here is followed by için, and nouns before için often stay in their basic dictionary form.

So:

• çay = tea
• çay için = for tea

You do not need the accusative here.

Compare:

• Çayı içtim. = I drank the tea.
  Here çayı is the direct object, so accusative is used.
• Çay için teşekkürler. = Thanks for the tea.
  Here çay is part of the phrase with için, so no accusative.

Yes. In Turkish, just like in English, short expressions of thanks do not need a full verb every time.

• Çay için teşekkürler.
• Yardım için teşekkürler.

These are perfectly natural as standalone expressions.

If you want a fuller version, you can say:

• Çay için teşekkür ederim.

But the shorter version is extremely common.

This order is the most natural one for this expression:

• Çay için teşekkürler.

Turkish word order is flexible in some contexts, but fixed expressions often have a usual order, and this is the standard one here.

A learner should memorize:

• X için teşekkürler
• X için teşekkür ederim

That will sound natural.

It may be understandable, but it is not the normal way to say it.

The natural Turkish pattern is:

• Çay için teşekkürler.

Putting teşekkürler first sounds unusual here. For a learner, it is much better to stick to the standard pattern.

It comes from teşekkür plus the plural ending -ler:

• teşekkür = thanks / gratitude
• teşekkürler = thanks

Even though -ler/-lar is the plural suffix, in expressions like this it functions like thanks in English, not literally multiple thanks in a mathematical sense. It is just the normal idiomatic form.

That is why Turkish often says:

• Teşekkürler. = Thanks.

Both can be used to express thanks, but they are used differently.

• Teşekkürler = thanks
• Sağ ol = literally something like be well, used as thanks

Sağ ol is more personal and informal. You usually say it to one person you are on familiar terms with.

Examples:

• Çay için teşekkürler. = neutral, natural
• Çay için sağ ol. = more informal and personal

For polite or neutral situations, teşekkürler is safer.

A rough pronunciation guide:

• Çay → chai
• için → ee-chin
• teşekkürler → roughly teh-shek-kur-ler

A few important letters:

• ç = ch as in chair
• ş = sh as in shoe
• ü = a front rounded vowel, like German ü or French u
• ı = a vowel that does not exist in English; it is not ee

A rough full version:

• Chai ee-chin teh-shek-kür-ler

It is a general pattern. You can replace çay with many nouns:

• Kahve için teşekkürler. = Thanks for the coffee.
• Hediye için teşekkürler. = Thanks for the gift.
• Her şey için teşekkürler. = Thanks for everything.

So the useful structure to learn is:

• [noun] + için + teşekkürler

Yes, absolutely. It sounds natural and common.

For example, after someone gives you tea, coffee, food, help, or a small favor, X için teşekkürler is a very normal way to respond.

Depending on the situation, a speaker might also say:

• Teşekkür ederim.
• Teşekkürler.
• Sağ ol.

But Çay için teşekkürler is a completely natural everyday sentence.