Che cosa significa “amikor iskolában vagyok, elszigeteltnek érzem magam más diákoktól" ，in this sentence,elszigetel is a verb,elszigetelt is it's past tense ,but why we add the nek to the word,Does it change a adj. to a adv. like ve/va changes a verb to a adverb? ?

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The phrase "I feel in some way" can be translated as either "valahogyan érzem magam" (with "valahogyan" replaced by the word, e.g. "szomorúan", but the suffix is kept), or "valamilyennek érzem magam" (likewise, for example "boldognak")

In this case the first version ("elszigetelten") sounds a bit awkward, so people would say the second one ("elszigeteltnek"). The point is that the suffix ("-nak/nek") has to be kept as that is the thing that indicates which word acts as the adverb to the main verb. It doesn't matter if the adverb in this case is a verb in its own right, as you noticed.