I'm not sure I fully understand your first question. Admissions officers for part-time programs will expect that you have a full-time job if you apply to a part-time or executive MBA program. If you're unemployed, they will almost certainly ask why you're not working and what you're doing instead of a full-time job.
Re: your GMAT score, schools look at your highest score. So, there's not really any downside to taking the GMAT again if you think you can do better. At worst, you'll end up sending a lower score, which the schools will ignore.
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