Learn Turkish: Alo, kim arıyor? - Hello, who is calling?

Alo is used almost exclusively for answering the telephone in Turkish. You would not use it to say hello to someone face-to-face; for that, you would still use Merhaba or Selam.

I learned that aramak means "to search". Does it also mean "to call"?

Yes! The verb aramak is very common and has two main meanings: "to look for" and "to call on the phone". Because of the telephone greeting Alo, we instantly know it means "calling" in this sentence.

The verb root is ara-, so why is it written as arıyor and not arayor?

This happens because of a rule called vowel narrowing. When a verb ends in a wide vowel like a or e, adding the present continuous suffix -yor causes that final vowel to narrow into ı, i, u, or ü. So, the a in ara- changes to ı, giving us arıyor.

Do I need to add beni to mean "who is calling me"?

No, you do not need to add beni (me). Just like in English, asking Kim arıyor? (Who is calling?) is perfectly natural on its own when answering the phone because the context makes it obvious.