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Just need to clarify what you're trying to do, since I've never used Illustrator.
1 - This is a freehand line drawn with the Pencil/Freehand tool? Usually, for detail, the thinner the line the better. Are you saying you want to scale a path smaller but you don't want the path to become thinner?
If that's the case, I think I know what's happening. On the Selection tool
control bar (
), the 4th button from the right (
) needs to be disengaged. (I think it's engaged by default.) You can hold the mouse over the button for a second or 2 and some little text will show up, that explains what any option will do. So for that one, when you scale a path, the width will stay the same.
Or are you using the Calligraphy tool? Are you using a graphics tablet with pressure sensitivity?
If that's not it, if you can explain a little more, we'll get there
2 - Yes. When you use either the Pen/Bezier or Pencil/Freehand tool, on the control bar, you'll see a small dropdown menu labelled "Shape:" If you set that to None, those tools will always draw lines with the same width all the way along the length of the line. From there, there are 2 or 3 ways to adjust the width. And these instructions are for versioin 0.91. Before 0.91, these things are different.
Select a regular path and go Path menu > Path Effects. Click the blue plus sign (
) and then you'll want to choose either Pattern Along Path (where you can draw your own custom triangle shape, to create the variable kind of width you want) or Powerstroke (which is a live-on-canvas way to adjust the width manually/visually). See Help menu > Inkscape manual, to find info on those. Go to the Comprehensive Index and find Pattern Along Path or Powerstroke.
With version 0.91, Triangle In and Triangle Out, in the Shape dropdown menu will automatically apply the Powerstroke. Then you just drag those pink nodes to adjust the width. Note that the pink nodes can be very hard to see.
The Ellipse option in the Shape dropdown applies Pattern Along Path automatically.
Or are you using the Calligraphy tool? Are you using a graphics tablet with pressure sensitivity?
3 - So in Illustrator, dragging an object copies it? Is it done with a key shortcut, or does it copy everything that's dragged? Typically in computer graphics, Duplicate is used instead of Copy/Paste. If you duplicate something, the new object is right on top of the original, then you can just drag it to wherever you want it be (or use arrow keys or whatever, there a few ways to move objects). There's a key shortcut for duplicate, but I don't know what it is (I tend to use buttons whenever I can). You can find the key shortcuts in Help menu > Key and Mouse Ref (need internet connection) or else the key shortcut is given in the menu item or in the tool tip (the little text that shows up when you hover the mouse over a button).
And finally, the very best tip for new Inkscape users is the Status Bar, which is the bar across the bottom of the window. And specifically, the notification area, which is the middle part of that bar. With the Selection tool engaged, the notification area will tell you what kind of object you have selected. When you're working on a complex image, that's incredibly important to be able to identify exactly what is selected. And with other tools, that area will give you hints and tips to what you can do next.
This can also be helpful for new users:
What To Do When a Tool Stops Working (or Tools are Drawing Invisible Objects)Let me know if I misunderstood something
