1 -- I would need to know the settings you have enabled/disabled (on the control bar), to try to see the problem it sounds like you're having. (The last time I tried that tool, I think I found the bug in the Orthogonal/Polyline mode....although I can't seem to reproduce it at the moment.) However, I would suggest not using the Connector tool. It seems to have at least one bug. (To be honest, I'm not sure why developers don't just remove it entirely, at least until they can fix it, since this is rather a glaring bug.)
You can use the Pen/Bezier tool or even the Pencil/Freehand tool, and get the same results in the end. Although I realize it has some helpful features, which the Pen and Pencil don't have, I think it will be less frustrating in the end, to not use it.
But let us know how you have the tool configured, and I'll try to answer your question. I don't really know without doing it myself, in this case.
2 -- Is this problem happening when you're using the Connector tool? Or is it a separate problem? Please tell us exactly what you're moving with the arrow keys.
Are you using 0.92.0? Or something later? The current stable version is 0.92.4. I know it doesn't seem like that big of a jump, but the "point releases" are all bug fixes (in Inkscape, right now). So if this is a bug, we need to know the specific version, to help us track it down.
If the file you're working in is large, let's say over 1 or 2 mb, and you're trying to move everything in the file at once, then the crash is probably a performance or resource issue. Or if you're moving just one object, but it has hundreds of nodes, that could do it as well. We can give you tips to avoid the crashing, if this turns out to be the cause.