Well I don't know WHAT the hell most of that means but I'll just wait a while.
DFHack is a hack: it inserts itself into the DF game by replacing one of the DLL files. If this DLL was compiled by Toady alongside the rest of DF, it would Just Work.
This is only true on Windows, where DFHack is implemented by replacing SDL.dll. Toady doesn't compile this, but it can safely be replaced (assuming the replacement is built correctly), since it's linked to DF dynamically (i.e. DF doesn't rely on a specific copy of SDL.dll).
On OS X and Linux, DFHack is built as a separate library and a modified launcher script is used to load this library before starting DF.
The reality is that the DFHack team has to poke around inside each new version of DF and find out where everything is stored, a task made a bit more difficult by the security features of Windows, OSX and Linux. When you hear references to the SYMBOLS table, that is the list of memory locations for game data (the in-game date, the raws, the name of a creature, etc., etc., etc.).
There aren't really security problems, since DFHack and DF run in the same address space (and can access the same memory).
Of the things you listed, the date is the only one actually in symbols.xml (cur_year, cur_year_tick, etc.). If I understand correctly, most other things are located with respect to an offset in symbols.xml and the size of certain structures (for example, "world" contains a list of units, each of which have a name which can be located based on the known layout of a unit).
A lot of addresses in symbols.xml can be located automatically with scripts (i.e. by scanning the executable). Some need to be located when DF is running, which can be done semi-automatically with a DFHack script. A few (debug flags and save_on_exit) need to be located manually. The bulk of the manual work is determining if there are any changes to structures. For example, 0.40.15 added four new types of announcements, which increased the size of the announcement_flags array. It's difficult to say what would have happened if DFHack hadn't been updated to take this into account, but less trivial changes can easily cause crashes.
I know that Dwarf Therapist also uses the SYMBOLS table, and a lot of 3rd-party tools (TWBT, Stonesense, Embark Tools, etc.) are DFHack plugins that can't operate without DFHack.
Dwarf Therapist actually uses a separate configuration format (not symbols.xml) which contains some different data, so there isn't really a single "symbols table". However, a lot of this data comes from the
df-structures repo, which is what DFHack uses as well. (It's also possible to generate a DT ini file using DFHack, which I did for 0.40.15.)