I have dealt with several of these cases. You need to contact your unit ASAP, and see if they can arrange an alternate duty location for you. If not, regardless of the logistical problems you need to report. The long term negative implication of an Other Than Honorable Discharge (which is what you will get if you don't report) are significant and far outweigh any logistical issues. Make sure all your paperwork is in order. You might want to contact a military law attorney prior to...
While possible, it is extremely unlikely. You essentially have to prove "exceptional meritorious service" during the time of your enlistment, which almost (if ever) happens. As for your second question, and ELS is reserved for 180 days or less. I suppose their could be some glitch or exception to that, but I have never seen it.
You cannot sue the Marine Corps. There are few areas of the law clearer than this. If you received a negative discharge you may be able to upgrade that discharge based on the misinformation you received.
Every case is different, but keep two things in mind. Less than 10% of all discharge requests are successful, and you have 15 years to apply. In many cases it is better to wait and increase your chances of success by showing post service accomplishments. I recommend you have one of the lawyers here on AVVO review your discharge packet and give you an opinion as to the likelihood of success at this time.