If fruits were picked by a Cohen for themselves and then someone else eats (with the Cohen's permission, of course), does the person still need to separate Ma'aser?
Short answer: Yes.
Long answer: Firstly, a Cohen gets Teruma, not Ma'aser, technically. (Though in Ezra's time they could [also] be given Maaser.)
Secondly, all fruit grown in Eretz Yisrael is Tevel until tithed - i.e. all Terumoth and Maasrot or taken off - no matter who grows the fruit.
Therefore, Cohanim may not eat Tevel, even if they want to eat fruit from their own trees.
However, a Cohen can keep the Terumah he separates from the fruit he picks or grows. He needn't give it to other Cohanim.
קכג: כֹּהֵן אוֹ לֵוִי שֶׁמָּכְרוּ פֵּרוֹת תְּלוּשִׁים, קֹדֶם שֶׁתִּגָּמֵר מְלָאכְתָן, וְאֵין צָרִיךְ לוֹמַר אִם מָכַר בִּמְחֻבָּר, הֲרֵי הַתְּרוּמָה וְהַמַּעֲשֵׂר שֶׁלָּהֶם