I feel the opposite, that 'you are looking inside for a writer' has more emphasis in the English on where you are looking. But English is ambiguous by nature, and they should probably both be accepted
Hmm, not exactly sure about the English part, but I'd say, that "You are looking for a writer inside", would be the English sentence that emphasises the inside part more (the Hungarian sentence emphasises the fact that you are looking inside, and not the part that you are looking for a writer).
Same verb, two different conjugated forms. Keres is third person singular, keresel is second person singular (both being indefinite conjugation forms, more about this later :D)