First of all, "absetzen" has several meanings but none of them would work for a pencil. The verb should be "ablegen" (to put down). Secondly, since it answers the question of "Wo?" (Where?) it needs the dative case, so it should be "auf dem Tisch". (If it's supposed to answer the question of "Wohin?" (Where to?, i.e. direction of movement) which needs the accusative, you'd just use "legen": "Ich lege meinen Bleistift auf den Tisch.") And most importantly, yes, it would be possible to move the prefix, but a) not to where you moved it, b) it would demand a comma, and c) it would need a larger part of a sentence following, e.g. "Ich lege meinen Bleistift ab, auf dem Tisch, auf dem sich bereits die Zeitungen und der Block befinden." Hope this helps.

No, it is wrong. The construction of the sentence is not right. :)