I think "Are you looking for a telephone?" is more like "(Egy) telefont keresel?", and "Will you (please) look for a telephone?" could be translated to "Keresel egy telefont?". Especially with her intonation in the current audio.
"Keresel egy telefont" - when you need a phone, any phone
"Egy telefont keresel" - when you are looking for a specific phone
This is just a guideline, not a rule. Not even close. It's all about context and emphasis.
"Keresel egy telefont?" - Yes/No question. Are you, or are you not, looking for a phone?
"Egy telefont keresel?" - Selection. What are you looking for? Is it a phone you are looking for?
It seems that, in questions, the inquiry is on what is at the front of the sentence. If a verb is in front, it is a yes/no question:
Kérsz kávét? - Do you want coffee? Yes or no. "Igen, kérek".
Kávét kérsz? - Coffee, or something else? "Nem, teát kérek".
Well, are they the same in English? The answer is, in some contexts they are the same. In others, you can't substitute one for the other. That is how synonyms work. :) And it is the same with their translations. In some contexts, they translate to the same word in Hungarian. In others, they do not.
Just one example: "look for this man" and "search this man" are quite different activities. They would be very different in Hungarian, either.
But "are you searching for" and "are you looking for" seem to be the same indeed, in Hungarian. So, both should probably be accepted, if that is what you are asking.