No, Ash didn't send his Gible to Professor Oak.
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Pikachu was in the Poke Ball that Ash had received from Professor Oak.
Professor Oak told Ash to get the GS ball and met Tracy. Ash entered the orange league and won then went back to prof oak and Brock stayed there with a professor called Ivy. Ash gave him the GS and Tracy was fascinated to see prof oak and wanted to stay with him
May's full name on the Pokemon TV show is "May" since she does not have a last name like Ash Ketchum, Ash's Mom, Professor Oak and Gary Oak do.
Ash went to the Orange Islands because Professor Oak asked them to go on an errand for him in order to retrieve the GS Ball from Professor Ivy however Ash also wanted to head to the Orange Islands about learning about the Orange League.
ash's gliscor status is currently unknown but its shown in the battle with paul in the sinnoh league after that episode its unknown it was left with professor oak or returned to McCann.