@trekiej
You can look up patents and registered trademarks in the US at
http://www.uspto.gov. Trademarks don't have to be registered, though, which is why people hire attorneys to determine whether or not a particular trademark exists before deciding whether or not to claim it for themselves.
Any work (and "work" has a very loose definition) created by anyone--person, corporation, whatever--is automatically copyrighted. You don't have to claim it, it just is. In the US, the copyright extends 95 years beyond the death of the copyright holder. (Good for your kids, bad for everyone else.) I'm not sure how it works exactly for copyrights owned by non-individuals. I'm sure it's explained somewhere at
http://www.uspto.gov.
Trade secrets are the intellectual property, processes, secret handshakes, executive washroom keys, etc. that someone--person, corporation, whatever--has not made public. Sometimes, even "public" information can be considered a trade secret, hence the trouble surrounding leaked details on various Apple products.
Amiga, Inc. (Delaware) owns various Amiga-related trademarks, including one for "providing on-line forums for transmission of messages among computer users concerning computers and computer technology." That means amiga.org, amigaworld.net, et al could, in theory, be subject to a trademark infringement claim if "Amiga" were used without permission.
The orignal Amiga trademark is still listed as being owned by Amiga, Inc. (Washington). Funny how the record was never updated. ;-)
Regarding reverse engineering, read the following:
http://en.wikipedia.org/wiki/Clean_room_designhttp://en.wikipedia.org/wiki/Reverse_engineeringEDIT: Interesting note: The Workbench trademark was abandoned, so there's probably no reason it couldn't be used by MorphOS, AROS, or another project.
EDIT 2: And someone apparently registered a t-shirt slogan: "AMIGA Ask Me If I Give A-shit"