Hello! I am new Ikscape user, came from Illustrator.
In AI you can edit existing path just draw some new path near the point or segment of the old one, which you want to change. I cannot find in tutorials, FAQs and books avaible in web anything about it in Inkscape. As I understood - the way is to edit nodes with tool - it seems to me take much more time. Please help me, may be anybody solved this problem.
Sketch mode of as I know, works during drawing, not after the first edition of path is done.

If you want to "continue" a path, select it, then choose and click on one of the ends of the path.

If you're coming from Illustrator, I recommend you take a glance at my quick guide. I had been using Illustrator before Inkscape and the guide was a way to familiarise myself with concepts I already knew from Illustrator.

microUgly, thank you for the aswer! I took a glance at your quik guide, but, to be true, a lot of its contents I've read before.
I use a tablet - so it is more comfortably for me to use Pencil = Freehand tool, no Bezier curves tool. I'll try to explain, what "edit mode" I wish to use: my aim is to make the outlining of photography. I have many TEM(=transmission electron microscopy) images of the sections. And I don't want to print them all and make the schemes with HANDS and real Pencil . My way is to use Tablet, digital images and Inkscape - to draw all cell borders in the layer above photo. And I may make a wrong curve - so would like to edit it without "Nodes edit tool" - just draw right way path's segment instead of wrong one.
The English is not my native language, so, please, let me know, if something is hard to understand in my topic.

The same method I described for is also true for

Alternatively, with the object you want to continue selected, hold Shift as you draw a new line and it'll be included as a part of that object without requiring that you start at an existing end.

Editing nodes might be unintuitive, did you know you could modify the path between the two nodes simply by dragging it (with Node tool). There is also a button on the Node toolbar where you can turn on permanent path outline, it can help when editing wide strokes.

Also look into Spiro paths, it's usually said they are more intuitive for non-technical users. Read more about the in the guide

Thanks a lot for your answers. I have found the solution of my some special paths editing - to use "Ctrl+/" - Division of paths operation.