I want to use Fritz 6 to analyze games that I input myself, and set up positions manually to play against the engine (for endgame training, for instance). For the moment, it seems I can only play complete games against the engine?

Any help most appreciated.

Whoa, been a long time, back in those days everything wasn't so user-friendly.  I seem to remember in some of those early versions you had to select the database function, and there was a menu item to enter a new game. 

Since its interface was based on Chessbase, I'd guess there is an option to set up a position, too, you just have to find it.  There may be submenus on the buttons at the bottom or something in the file menu to get there, sorry I can't remember.

Here's a couple of reviews of Fritz 6, but these reviews don't answer your question.

http://www.chessusa.com/fritz6.html

http://seagaard.dk/review/eng/sw_playing/cb_fritz6.asp?KATID=SW&ProductID=13&PUBID=CB&AUTID=3&BUYID=&ID=SW-Playing

I'm sure this is possible to do in Fritz 6 somehow.  Alas, I no longer have a copy of that old program.  (And I don't wish to look for it and download it.  I COULD find my old Fritz 8 CD and attempt to reinstall that program, since the method in 8 is probably the same as in 6, but I don't wish to do that either.)

Note that you MIGHT have to set up the position in a different program (WinBoard, for example) and then copy the FEN from that program and paste it into Fritz 6.

Have you considered upgrading?  I'm pretty sure Fritz 6 doesn't support outside UCI engines.  That feature came about later.  The newer versions all support any UCI engine you choose, (Houdini, Stockfish, Rybka, Critter, etc.) in addition to a host of other new features.

Here's the Fritz 6 manual in italian, Dutch, Spanish, French, and Sweden:

http://www.chessbase.com/download/pdf/F6_ITAL.PDF
http://www.chessbase.com/download/pdf/F6_HOLL.PDF
http://www.chessbase.com/download/pdf/F6_SPAN.PDF
http://www.chessbase.com/download/pdf/F6_FRANZ.pdf
http://www.chessbase.com/download/pdf/F6_SCHW.pdf

Suprisingly, I can't find it in English!!!