1. Are we allowed to get married on an army base that isn't his own?
Yes you can get married on any military base, just contact the Chaplain at that base.
2. What are some recommendations on how to plan this wedding?
Thousands of people get married in Hawaii every year it's all online, It really boils down to how much you want to spend. Hawaii requires you to be in Hawaii for a few days in order to get the marriage license please check with them to prevent getting into a snag later. I was married there, I would recommend paying the extra to get the video... they splice in some really nice Hawaii video. The Hale Koa (Military hotel in Waikiki) does a wedding package, it's really a nice place and priced right too. Having non-military guest stay there is tricky but local hotels are near-by for them.
3. Since I was moving to Hawaii (Schofield Barracks to be exact) I was wondering what are some good places to live at and what are some good colleges?
As you most likely know, it's very expensive and small but everyone finds something... If they have military base housing that would be another option for you after you're married. Getting your belongings moved there on Uncle Sam's dime and your airline tickets requires you to be legally married prior to his PCS move. Try the U of H.