Learn Turkish: Markette elma, portakal falan aldım. - At the market I bought apples, oranges and so on.

The word market ends in the voiceless consonant t. In Turkish, when a word ends in a voiceless consonant, the suffix that follows must also start with a voiceless consonant. This changes the standard in/at suffix from -de to -te. Because the last vowel in market is e, vowel harmony keeps the suffix vowel as e, resulting in markette.

Why are elma and portakal in their singular form here?

In Turkish, when you refer to a general category of items as the direct object of a verb (like buying apples in general, not specific ones), you typically do not use the plural suffix -lar or -ler. The singular form represents the whole category.

I learned that direct objects take the accusative suffix. Why isn't it elmayı?

The accusative suffix is only used for specific, defined objects, which translates to buying THE apple. Because the speaker is just buying general apples and oranges, the nouns stay in their plain, unmarked form.

How do you use the word falan?

Falan is a very useful, casual word meaning and so on, stuff like that, or or something. You just put it after a noun or a list of nouns to indicate that there were other similar things included that you aren't bothering to name.