Is it possible to attach a label to a line in the Google Drawings app

There is no automatic way to create a right-angled line. The best way to do this would be to:

1. Create 2 intersecting lines. I think you mention this in your 1st bullet. One way to make sure that the lines are perpendicular to each other is to hold the Shift key down while dragging out the line. This will automatically "snap" it to a preset angle (0, 45, 90 degrees, etc). By making 2 lines perpendicular you could make the ends meet and create a right angle line.
2. Use the polyline tool. You can find this by clicking on the drop down arrow next to the line icon. This menu will allow you to create lines of different types. Examples are:
   • Arrow
   • Curve
   • Polyline

Some of these new lines (not all) will allow you to attach the ends to the connection point of another shape (like a text box) but you'll have to fiddle around with it to find what solution works best for you.

If you're looking to create formal flowcharts with Google Drive, there are now apps you can connect to your Drive account that will help you create flowcharts. Examples include Lucidchart and Draw.io. To connect these apps to your Drive account, go into your Drive and click Create > Connect more apps

Google drawings are "single page", like a canvas.

You can insert drawings in documents, sheets, slides, Google Sites pages and web pages.

References
Paint and create charts and diagrams with Google Drawings - Docs editors Help