Learn Turkish: Resmî dil Türkçedir. - The official language is Turkish.

You could say Resmî dil Türkçe in casual conversation, but adding -dir makes it a formal statement of objective fact. This suffix is used in encyclopedias, news, and official rules to state absolute truths. Since we are declaring a country's official language here, -dir is the perfect choice.

What is the hat symbol over the 'i' in Resmî?

That symbol is called a circumflex. In Turkish, it is used on certain loanwords (mostly from Arabic or Persian) to show that the vowel should be pronounced slightly longer. It also helps tell words apart: resmî means "official", while resmi (without the hat) means "the picture" or "his/her picture".

Since Türkçe is a proper noun, shouldn't there be an apostrophe before -dir (like Türkçe'dir)?

Normally, you do use an apostrophe to attach suffixes to proper nouns (like Türkiye'dir). However, there is a special spelling rule in Turkish: if a proper noun was created by adding a suffix to another word (like how the suffix -çe turns Türk into the language Türkçe), you do not use an apostrophe for any extra suffixes that come after it.

Where is the word for "The" in this sentence?

Turkish does not have a definite article like "the". The phrase resmî dil translates literally to "official language", but depending on the context, it translates to English as "the official language" or "an official language".