Welcome to the forum!
For making a regular stroke tapered, you can select it, and then Path menu > Path Effects. From there, you can either use Powerstroke, or Pattern Along Path. Powerstroke is probably easier, and since it will take much less typing, I'll focus on that.
After you select Powerstroke from the menu (click the big blue plus sign to open the menu), it might look like not much happened to the stroke. But if you look very closely, you'll see some new pale pink nodes on the path. (They are hard to see.) Grab one of those and drag, and you'll see that portion of the path will get wider.
If you need extra pink nodes, position the mouse over an existing node, and then Ctrl + click. The new node is right on top of the original node. So you can just drag it away, and place it where you need it. If you need to remove pink nodes, position the mouse over the one you want to remove, then Ctrl + Alt + click.
Note that the tutorial is probably using something like Pattern Along Path.
For your other question, I think you are asking for Path menu > Difference (although I'm not positive). However, if you have used Powerstroke on the objects which you want to use Difference on, you'll need to select them, and then do Path menu > Object to Path. After that, Difference should work. If I understand what you're asking, there are probably other ways to accomplish that.
By the way, there are hundreds if not thousands of Inkscape tutorials around (check out our Home tab).
