Several related Newbie questions
> 1) How much can I do working in the Sandbox? I noticed some extensions that seem like they would be useful.
Do you mean  or do you want to build your own sandbox? In the latter case you have to follow the installation instruction from SMW and any of the extension you want to use in addition.
If you are unfamiliar with the technical management of MediaWiki but eager to evaluate whether SMW can provide the environment you are looking for or not then I would suggest you use  as test environment. We provide  for users who want to try out SMW or evaluate new features we develop with newer SMW releases therefore  runs with a higher version.
> 2) I've heard a lot about Dublin Core and it seems like the right model to use for things like books, journal articles, videos, etc. to store all the metadata (authors, date created, publisher, etc.) about them. That seems like such a common possible requirement I was wondering is there any way to load a vocabulary for Dublin Core into my Sandbox environment
Since we are rely on MediaWiki we have to account for the management of those data in certain ways (different from what you are use to in comparison to Protege). Importing vocabulary provides an introduction on how external vocabularies can be imported with [2, 3, 4, 5] containing some definition examples for the DC/FOAF/DWC namespace.
> 3) As I said I've developed several ontologies in OWL using Protege and also using the Semantic Web Rule Language (SWRL). Ideally, I would like to develop an ontology and import it into my SMW environment. Is that possible?
Depending on the features you used for the ontology, that should be possible except for SWRL related elements. See above about the importing of vocabularies.
> Just inverses, subclasses, but not things like transitive properties, DL definitions for classes much less SWRL rules. It's not a deal killer if this isn't supported but I just wanted to double check to make sure I'm understanding things correctly.
Yes, transitive properties are not supported as that would require a reasoner which is not part of SMW core. If you are using a SPARQL instance as query backend that you may query instances that rely on a reasoner  in connection with a selected triple store.
> I would still like to load OWL ontologies. Again wondering if that can be done with a Sandbox environment
As I said above, try using  first before starting your own server so that you can get a feel for the environment and see whether it fits your expectation or not.
We deploy some standard vocabularies with each installation to make it easier for users to start reusing them where they see fit.
I hope this answers some of your questions, in regards to SMW and while less directed towards ontologies and OWL, the following video playlist [8, 9] may give an insight as to what and how SMW works.
> portal for a set of related topics in cognitive science for a non-profit. We have a budget so I could use a commercial tool, I'm looking at Pool Party and Open Calais as well. I'm pretty technical but more at the level of OWL and
If the project somehow doesn't meet your expectation maybe you can tell us about those shortcomings so that we may take them into account for future refinements.
-  https://sandbox.semantic-mediawiki.org
-  https://sandbox.semantic-mediawiki.org/wiki/Sp%C3%A9cial:Version
-  https://www.semantic-mediawiki.org/wiki/Property:Dc:identifier
-  https://www.semantic-mediawiki.org/wiki/Property:Foaf:knows
-  https://sandbox.semantic-mediawiki.org/wiki/Attribut:Dwc:kingdom
-  https://terms.tdwg.org/wiki/dwc:kingdom
-  https://www.semantic-mediawiki.org/wiki/Help:Transitive_relationships
-  https://www.cs.ox.ac.uk/isg/people/yujiao.zhou/aaai2014/paper.pdf
-  https://www.youtube.com/playlist?list=PLIJ9eX-UsA5cQY7T0ZmLI2ASdea3ffrvG
-  https://www.youtube.com/edit?o=U&video_id=ZsNMFpNfUdE