Is it possible to have a simple passive SFP/SFP+ bulkhead passthrough connector, with two female SFP/SFP+ sockets facing opposite directions and wired directly together, for a data cable entering a dust and humidity controlled rack cabinet?
First, you have a fundamental misunderstanding. There is no such thing as SFP/SFP+ "sockets" (unless you count the "cages" SFP/SFP+ are inserted into) or cables (excluding "direct-attach" types of SFP/SFP+ like Twinax). SFP/SFP+ are transceivers in a modular form. They are active electronics and do not function without a power source.
The connector type for nearly all SFP/SFP+ transceivers is LC for fiber and 8P8C (commonly referred to as RJ45) for copper solutions. These are what I believe you are actually asking about. As such, it is possible to have a LC/LC or 8P8C/8P8C "passthrough" connector as you describe, but generally speaking this is frowned upon. Throughout the rest of my answer, where you ask about SFP/SFP+ cables/connectors I will answer substituting LC/8P8C in it's place.
Rather, look for a cable penetration solution for the NEMA and/or IEC rating to which you are trying to meet. There are a wide number of solutions on the market that provide for cable penetrations while maintaining these ratings (all the way to fully submersible). Use such a solution when passing cabling into your rack/cabinet.
Are copper SFP/SFP+ cables simply a passive straight-through cable, or are there active electronics involved?
The cables themselves are passive, however the SFP/SFP+ are active (even if they are described as passive, they still require being inserted into a powered device).
Would it be possible for an SFP/SFP+ fiber module to be joined to a copper SFP/SFP+ cable with a double-ended F/F SFP/SFP+ socket and function properly?
No. Put as simply as possible, they speak different "languages." Fiber uses light to pass data and copper uses electric current. There is no way copper and fiber can pass data to each other without some sort of (active) device to bridge the two.
And likewise, could two copper SFP/SFP+ cables be joined together with a double-ended F/F SFP/SFP+ socket?
Again, possible, but likely to violate the standards of proper cabling and could introduce problems to the data communications. Generally speaking, you should be avoiding an splices, couplers, etc. These types of "solutions" may be used in a short term fix, but should be highly avoided for permanent solutions as they may introduce issues that will likely to be difficult to troubleshoot/diagnose later on.
Is there such a thing as a copper SFP/SFP+ extension cable, with an SFP/SFP+ socket on one end? If none currently exists, could it work?
This is really just a form of mechanical splicing. It could work, but again see my answer to your last question.