Yes
There are. Most the jobs listed on this site are actually single-site jobs that don't require any travel: http://www.nursingjobs.org/hawaii
There are several travel nursing jobs available in Hawaii. Jobs can be found on sites like hawaii-hi.nursing-jobs.us/. There are some companies hiring for such jobs in that area. You can visit www.careerbuilder.com or www.monster.com to find one appropriate for you.
Most school districts have a link somewhere on the district website listing any available jobs.
Get in contact with their human resource department, they can inform you of any open jobs, or point you in the direction of something you can do in the meantime if there aren't any open ones.
Yes
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Yes there are engineering technician jobs open. Without knowing what field of engineering you are interested in it is impossible to steer you in the right direction.
There are specific magazines and websites that tailor to jobs that are located in Hawaii. Sites like Hawaii Business list a number of the top companies to work for in Hawaii.
There are multiple military bases where you could enlist. If that is not an option, there are plenty of travel agencies you could work at in any position!
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They're appointed.