Yes.. Exactly 7 days only. Just go to local immigration office. Basically it's a denial of extention stamp that gives you 7 days to get out of the country. Cost is 1900b. Bring same document you used to extend first time.. Should have no problem.
I highly encourage you to walk into the elite office and talk to them.. Not email. Sometimes (often) they give wrong information and "sales agents" online really do not know...
The best thing you can do is talk to a hotel that you will staying at, they might be willing to store it for you for a while for free.
There are luggage storage places at the airport, and some of the self store places offer luggage storage.. But they are all ridiculously priced high.
There some self mixed type storage, where they pickup that use standized boxes and store it in a warehouse and the delivery on demand.. If your suite case will fit in one that probably a cheaper and convenient option.
Google, luggage storage Bangkok, storage pickup Bangkok, for more information.
Duke is well respected.. But doesn't work for everyone. They use the immersion method of teaching. If you didn't already they should allow you to sit in on a class before enrolling. They have classes online still too.. If you want to try another same building is ALA, good school still but doesn't use immersion method.
If your business is publicly trade or does at least 150m (usd) a year in revenue.. Yes. Otherwise no. Funny exception that the business you work for has to be larger and well established.
You can go under wealthy status if you have at least 1m in net worth.