I'm stuck trying to figure out how to turn elements of a drawing into objects:

I used Inkscape to convert a simple back-and-white drawing into a vector drawing. Then I saved the vectorized version as an svg. When I reopen that svg in Inkscape, I can't select individual elements within the drawing and turn them into objects. Am I trying the impossible?

Everything is an object in inkscape. I'm guessing your original black and white drawing was a raster image that you converted to paths.
This vectorised object is a group of paths that can be separated to its elements by ungrouping it. Select the group and press Ctrl+Shift+G, to achieve that.
Note that by default the group is placed above the original image, that you might not want to use furthermore.

Lazur,

I should have been clearer about the original artwork; yes, as you guessed, it did indeed begin as a raster image. Thanks for your feedback. The ideas you raised helped me figure out an approach; for those beginners like me, who may have a similar problem in the future, here is my solution:

First, (with an SVG file) go File/Open; then Edit/Select-All. In my case, after the selection, a dialog at the bottom of the screen then said "Path 8128 nodes in root."

Next, go Path/Break-Apart. For me, a dialog at the bottom of the screen then said "564 objects of type Path in root." In my instance, the drawing now has numerous dotted-line boxes, each one surrounding a unique path. My black-and-white drawing has graphic elements that I want to isolate, and are composed of multiple paths intersecting one another, but these areas of paths' intersection now appear blacked-out, like big, black "blobs" -- yet just temporarily, as you will see. If you try to select anything at this point, you will only be able to select the full image as one big object. So, Edit/Deselect.

Now, any path or collection of paths can be selected and processed in any appropriate way. After processing -- for instance, re-sizing or moving -- the selection still remaining can be recombined with Path/Combine, at which point the selected-processed "black blobs" will resume their correct appearance.

Any other ways of doing this?

Would not suggest to uncombine the path for editing as with the "blobs" style you get overlapping paths. Even if all have the same colour and some transparency, it's not giving the feel of the actual drawing's.
You can use the node editor tool for this purpose without the unkombining.
Maybe it will be a bit slow because some 8000 like nodes is too much for a regular inkscape svg drawing.
It depends on the original image, that what you want for the final result.
Auto-tracing never gives you as good result as if you redraw it with the path tool.
If the auto-traced version is good enough, you can try the simplify path option to make the path have less nodes.

So the traced image is already a path.
Select all the text and go to Path - Break Apart.
Usually the letters with centres get filled in.
Select that letter (drag a box around the outside of the letter and the centre) Meaning select both the letter and the filled in space, maybe use the arrow and hold Chift while selecting .
Now go to Path - Difference
To repeat, use the top arrow, holding shift while selecting both parts of the problem letters which had been filled ( the outside and the fill ) , then selecting Difference or Exclusion removed the fill.

Play around with it, that should do it. This advice is for if you took a image from offline, and traced it, and wanted to brake apart the image into its separate parts so you can edit it more easily.

Another approach is to copy your traced image, then draw a rough shape that covers one of the parts you want to separate out. Select both the new shape and the copy, then use Path > Intersection to remove all of the copy except the area that was covered.

Repeat for each section of the image, until you're left with all the parts separated. This works best if you only want to split it into a few parts, and if there's a clear separation between them.