Welcome to the forum!
If you don't see the path connected to a node when you drag it, that could be happening as part of performance issues. Do you see this behavior in a new blank file? Or does it only happen in very, very large files (say over 1 mb)? Do you have any other performance issue, such as slowness or freezing?
Just to make sure you have the right settings in Inkscape Preferences, go to Inkscape Preferences > Tools > Node and make sure "Update paths when dragging nodes" is checked.
Are you using that path outline feature (the annoying red line which flashes when the mouse goes over the path)? If so, you'll also want to check "Update outline when dragging nodes".
Or if you're a new user, I guess it's possible that part of the path is hidden under another object. Or that you're dragging the node underneath another object, so the path can't be seen. It could happen with any color of object, but if you have an object the same color as the background, you might not remember it's there.
To make sure the object you're dragging is on top of everything else, select it with Selection tool and click Object menu > Raise to top (or this button on the control bar
). Or if you're using Layers, in the Layers menu, click the tiny eye icon, to hide the upper layers.
I can't think of anything else to explain the path not showing, right now. If none of that helps, you might consider sharing your SVG file, and telling us exactly how to reproduce the problem (which node to drag and where to drag it).
Oohh.....It could be that you've accidentally drawn a path with an LPE applied to it. In that case, sometimes the path doesn't show up at all, whether you're dragging nodes or not. You can find out if the path has an LPE by selecting with Selection tool (
) and looking at the status bar. The status bar will indicate "path effect". If you see that, then you can do Path menu > Remove Path Effects (at the very bottom of the menu).
"Cusp node to cusp node" is probably the snap indicator. Once you learn how to use snapping, you'll probably (well, at least might) want the indicator to be functioning. So for now, you can just disable snapping. In the toolbar along the right side of the window, the top button enables and disables snapping globally. However, if you do want to turn off the indicator, it's at Inkscape Preferences > Behavior > Snapping and uncheck Enable Snap Indicator.