Sorry it took me so long to reply.
The only tool I can get this to show with is the FI select tool
That's correct. Other tools have different little icons or indications.
The problem with deleting the upper segment of the rectangle (and also why you can't join nodes), is because it is a rectangle shape, not a path. You may have noticed when you select it with the Node tool, you see 2 small squares and a small circle. These are known as the shape handles for adjusting the size (although you can also adjust the size with the Selection tool). Those are your clue that it's not a path yet.
(Note that previously when you used Path menu > Union, you did not have to convert to path first. Union automatically makes it a path. But if you don't use Union (or other path operation, aka booleans) you have to take the extra step to convert to path.)
Select it with the Node tool, and click Path menu > Object to Path. (Or there's an icon on the control bar which looks a little like a blue figure 8.) Then you'll see the shape handles are gone, and now you should see 4 nodes (tiny gray diamonds) one in each corner. When you see nodes, you know it's a path.
(If you draw a circle or ellipse, and convert it to a path, you'll see tiny gray
square nodes. The diamond nodes are called corner nodes and the square nodes are called smooth nodes. Corner nodes make sharp corners and smooth nodes make curves. When you click on a node to select it, you might see node handles (if the node has any), which are thin blue straight lines with a tiny circle on the end. Often there are no handles on corner nodes. But smooth nodes almost always have handles.)
Now with the Node tool, position the mouse over the segment that you want to remove (between 2 nodes). For this tool, the indication that the mouse is in the right place is a little hand. I think it's supposed to be a fisted hand. Or you could drag a selection box around both nodes, as well.
Click once, and you should see both of those nodes become highlighted blue. Now when you click on "Delete segment between 2 nodes" button, the segment will disappear.
Ok, so now that you have end nodes (on the end of an open path), you can connect them together. You can only....well, most of the time, you can only join nodes which are end nodes. And only 2 nodes can be joined. If you need a situation where 3 or more paths meet at a single node, you have to do some tricks.
In the situation you have in the attached file, the end nodes are a little distance apart from each other. If you join them from there, the new single node will be precisely between the original end nodes. Use "Join selected nodes" button on the control bar. Or there's an option "Join selected nodes with a new segment" which will draw a new segment between the nodes, leaving them where they are. Or you could use snapping to place one of the nodes precisely on top of the other one. Let me know if you need details about that.
Whichever way, you need to select both nodes first. There are a couple of ways to do that, and with more experience you'll develop your own preference.
One way is to click one node to select it. Press the Shift key (which allows multiple selection) and hold, while you click the other node (or however many nodes you might need to select). Another way is to use the Node tool to drag a selection box around both end nodes. If you use snapping to place the nodes on top of each other, dragging a selection box is the best way to select them. (It's very tricky to select them one at a time, when they are on top of each other!)
4. Yes and no. Ultimately the guide's placement is relative to the 0,0 origin. When you drag out a guide, you could have it snap to something, like one of the nodes of the vertical line. Double-click on the guide, to produce a little dialog box. (The mouse pointer changes to the "finger" icon, when it's in the correct position.) In the dialog is a checkbox for Relative Change. So since the guide is snapped to the vertical line, you could enter 0.5 inch in the dialog, to put it a half inch to the right (or -0.5 to put left of the line). (You should have your whole document set to inches. It is possible to use different units here and there, but most of the time you want the whole document set to the unit you want to use. Need more info?)
The other way to do it, would be to select the vertical line with the Selection tool, and notice the x coordinate. Then add the half inch, and that's where you would place the guide.
There's a fabulous feature for guides, Object menu > Object to Guide. So if you draw a rectangle, and click Object to Guide, Inkscape will automatically create 4 new guides where the sides of the rectangle used to be. You might find that helpful as well.
Or you might like to use a grid with snapping, to keep things organized and proportional.
5. Yes. 2 ways. Disengage the top button on the snap control bar (which is usually along the right side of the window). This globally disables snapping. Then click again to re-enable snapping. If you leave the top button engaged, you can disable snapping by pressing the Shift key
after you start dragging something. Most of the time, you can press Shift before you start to drag. But there's a conflict with the Shift key, if you are dragging a node. So you have to start the drag first, then press Shift, if it's a node that's being dragged.
6. You can format text in a few ways, but not in every way (which dedicated text programs such as word processors are capable). With the Text tool enabled, click once on the canvas and start typing. After the text is typed, look on the control bar for many different ways to format the text. There's a dropdown menu for the text size (although it's not labelled, except by tool tip). And another one for changing the font. There's also a Text and Font dialog, which is very large in size. A lot of people prefer to use it. For my needs, the control bar is enough.
Any more questions or clarifications, just ask