Rectangle with a dashed line on the left side

Is it possible to make a rectangle where the left side is drawn
with a dashed line, while the other three sides remain continuous?"

yes.
1) create rectangle first (using rect command, or using individual line drawing commands or using any other way)
2) select left line
3) set line type to dashed for that line using Modify Attributes or Properties command.
4) that's it

If rect is drawn as polyline - no, that's not possible, the linetype is applied to the entire entity (so polyline should be expanded to individual entities)

How does one select the left line?  

When I click upon the rectangle, the whole rectangle gets selected.  And when
I used modify-properties, the line-type affects the whole rectangle.

You have to use Modify-> Explode to convert the polyline into separate entities.

Right.  After exploding the rectangle, I get individual lines that I can select separately.

Is one supposed to recreate the rectangle using a block? I noticed that when using a
block, I can no longer select the individual corners of the rectangle.

Alternatively, I selected the segments and used 'Create Polyline from Existing Segments',
which preserves the ability to modify the corners, but I lose the dashed line style on the
left segment. With a polyline, it seems I cannot have different line types for individual
segments.

A Polyline is a single entity, which can only have one set of attributes.
A Block is a composition of multiple different entities where each entity can have its own attributes.
A Block can be inserted multiple times with different properties like scale or orientation.
The insert itself has attributes which do not modify the block's entity attributes. E.g. insert the block in a layer different from entities layer and see what happens when you make the layers invisible.
A Block can't be modified inside the drawing, because the drawing has the insert entity but not the block.
Use edit block to modify the block, there you can select single entities.
See https://docs.librecad.org/en/2.2.0_a/guides/blocks.html#editing-a-block

Are blocks the only possibility?

Have displayed the "Block List" and changed some other attributes on the right segment.

After using the "Select the active block in a separate window" icon, how can I get to the
full drawing again?

When making a rectangle, is the object a sort of polyline?