Inkscape // Trace Bitmap - How to select specific objects

If your traced image happens to contain something like this

I mean handwriting, where the letters are tied together like a continuous curve, you are out of luck. The only way to make major changes is to start from the beginning and write better.

That's because tracing has generated a colored area which has not a slightest amount of info where one letter ends and where the other starts. Also the writing path of the pen is lost, there's left only the inked area with no info how it was originally created.

In theory one could edit the edge path of the inked area (it's got a red stroke in the next image):

Believe, life is too short for major changes in this way. Write better. Scan and trace again!

Minor changes like making some letter a little thinner may succeed by editing the edge with the node tool or by subtracting a manually drawn shape by applying Path > Difference. Respectively one can add material by applying Path > Union.

A whole letter can be moved by selecting its nodes and dragging. The edges stretch like rubber. Sometimes the result needs only a little manual node editing to look good, but as well a substantial amount of node editing can be needed to make the text look regular again. An example:

All nodes of K are selected and moved slightly downwards by ticking the down arrow key. The transition from K to letter l was fixed by deleting few nodes. Do not expect it's generally this easy.

The situation is easier if your traced image contains separate letters like this:

It's a combined path. You can separate its parts by applying Path > Break apart.

See NOTE2 in the end of the answer. It contains an important addition

Unfortunately command Break Apart really separates every part. Also those shapes which were there to make the holes are now full black. The holes below them are vanished.:

Fix it by selecting everything which are on A and apply Path > Combine. The hole comes back:

After combining the parts of B, too, one can move the letters to new positions and make other edits:

NOTE1: If the parts are separate islands in your bitmap image, they probably can be easily selected, moved, scaled and rotated before tracing in GIMP, Photohop or other bitmap image editor.

Lettering by hand easily makes some letters to touch each other. The method above does not separate them, AB in the next image is still a single combined path:

In such case you have numerous options. One possibility is to at first duplicate the combined AB and then draw with the pen a cage (=a closed path) around your assumed A:

Select the cage path and the duplicate. Apply Path > Intersection. B vanishes from the duplicate. A is moved apart in the next image:

B can be recovered in the same way, but as well you can select the AB and delete all nodes of A with the node tool. The remaining shape is not perfect B:

But you can reshape it with the node tool. Adjust nodes and handles for the right edge form:

It can be useful also to delete excessive nodes. Too many nodes make the curves easily to look irregular and it can be difficult to keep curves smooth.

NOTE2: Mr. Billy Kerr has given in his comment a rectification: Using Path > Split path instead of Path > Break apart doesn't disassemble the holes in the letters. After applying Split path to ABC the letters are unbroken, but free for individual edits. Split path doesn't separate letters which touch each other.