It sounds like you might have a shape being applied to your paths. On the Pen tool control bar, which is the first row of icons above the horizontal ruler, make sure the Shape dropdown menu says None. Also make sure it's in Regular Bezier mode, and not another like Spiro Spline or other.
Sometimes seeing horizontal or vertical lines thicker or thinner than they should be is a display problem with Inkscape. Zooming can affect it too. Sometimes you might need to move a node, by just a pixel or maybe even half a pixel, to fix it. Yes, I know the angle would no longer be 90 degrees, but with just a pixel, it would still look like it was. But I'd want to see the SVG file before I was sure that was the problem.
Hhmm, I notice on your ovals, that the sides are wider than the top and bottom. I'm not sure how you did that, haha. Did you do it on purpose, or is that part of the problem too?
How are you putting the dot on the end of the line? Markers? You would need to move the paths first, and then apply the dot after you finish moving them. Sorry, I didn't know about the dot, when I explained about moving the paths around.
Unfortunately, I'm about to log off for the day (prior commitment) so I won't be able to make the video right away. But it looks like you're figuring out the Pen tool, and other things too, on your own. Using the grid with snapping is great way to keep the angles square! Besides the dot, is there anything else you're using, that you didn't mention yet? I would want to put that in the video too. I probably won't be back until tomorrow night, but I'll still plan on making it then, if you still need it.