Translation:Péter is looking for chairs, not tables.
So far Present tense in Hungarian can be translated by both Simple present and Present continuous. But NOT IN THIS CASE! I could not grasp why "looks for" IS NOT an acceptable translation for "keres".
Because it has not been added as an acceptable translation yet. Please report it, it is perfectly fine.
No. While very often you can expect that -ot is the ending for singular back vowel nouns, when in the plural the accusative is usually -at (back) or -et (front)
But in general a singular back noun will have either -ot or -at or just -t, as is the case with asztalt