The framerate for one of my programs slowed to a fraction of its earlier value when I (mistakenly) placed all the terrain 'chunks' at the same location - which wouldn't be a problem (easy to fix) except I'm wondering whether any overlap between objects would always slow the framerate, such as if I place trees right on the surface of the terrain, thereby causing a slight overlap for each. If so, this would cause severe problems unless the objects are adjusted so they have a slight gap between them.

In order to have a fairly large map, I need to have only a portion of the terrain in memory at a given time, and then update it as the user moves. I'm wondering whether it's better to : a) have a single object for the in-memory terrain and then add and subtract triangles from the sides as the user moves (is it possible to subtract triangles?); or b) divide the in-memory terrain into several chunks, each of which is a separate Object3D, and then when the user moves too far in a given direction, reposition these objects while deleting the chunks which are now well beyond the viewable area and adding new chunks on the other side. c) Is there a third option?

Wow.  What method are you using to generate the terrain, and how far does it extend in any given direction?

Since the built-in fog effect apparently works well only when the fog is 'black' (according to one of the files or wiki articles), what's the best way to produce atmospheric haze - i.e., making distant parts of the landscape look bluer? 

What do you mean by "handle"? Create or render it? For creation, have a look at this thread: http://www.jpct.net/forum2/index.php/topic,1343.0.html

  Thank you - that should be a big help. But if I'm wondering if there's any other way to do it, such as a 'heightmap' type 2D array separate from any 3D polygon objects?  I remember coming across a webpage that seemed to imply that something of that sort was possible, although I may have misinterpreted.

Does JPCT allow a program to generate 3D objects at runtime?