Command lines; Create a shortcut to Mapster32, right click it, select properties. Add
-jCustomT to the end of the command line... I don't remember if it needs to be inside the quotation marks or outside of them. If you use that shortcut it should point it to the directory containing your DEF. Otherwise, check mapster32.log again and see what it says.
Your DEF file should look like this;
include duke3d_hrp.def
dummytile 3585 32 32
texture 3585 { pal 0 { file "CustomT/Sprites/Posters_&_Pictures/3585.png" } }
Or possibly;
include duke3d_hrp.def
dummytile 3585 32 32
texture 3585 { pal 0 { file "Sprites/Posters_&_Pictures/3585.png" } }
As a last thought, it may be that the directory name
"Sprites/Posters_&_Pictures" is upsetting something, you might have to give it a shorter, simpler name and then update your DEF file to coincide with it.
I'd like to point two things out; Firstly, I don't currently have a machine capable of running this, so I'm somewhat in the dark here too. Secondly, props to you for posting a log file, a lot of people don't think do that.
DEF can be tedious initially, but once you get a grasp of the context it's not that hard. CON on the other hand (Changing/adding new enemies/behaviours/etc to the game), now that's a different story, but you don't have to worry about that.