Hi. In advance, some of these issues can be my mistakes, in this case I 'm sorry.
Modify--> Trim / Extend two option
1 The cut between two figures curves (circle, ellipse, or arc) is made according to where on each figure is selected. It can cut two, cut one (especially if it's between the ellipse and the circle cutting the ellipse like with the normal cutting option), and may also extend a figure (especially arcs) when you expected to be cut.
It seems that the application sometimes isn't sure lengthen or trim the curves, and if it has to cut one or two.
However, with the straight lines have no problem.
2 When you try to cut a circle or ellipse intersecting a closed polyline or a freehand line if you select these first, the application breaks and closes.
For your item 3: we have serious trouble with our equation solver. We will see whether we can improve it.
Have a look at this dxf file, with the red and green circles has similar meaning, and the intersections of those two circles are the two points to pass, and the white circles are the base circles.
a, start tangential circle 1_2p;
b, choose any white circle to draw tangential circles of it;
c, choose the two intersection points between the red and green circles.
ideally, the algorithm should be able to generate both red and green.
tan1_2p.dxfDraw--> Circle--> tangential 2points option
This option does not work as I expected. I wanted to draw a circle (green) tangential to the small white circle and then going through two points, the left upper and lower corners on the square, but the application draws the red circle. Indeed the two circles meet the two conditions (being tangential and passing through two points), but the application always draws the red circle. I don't know if this is a bug or can be configured differently to make the green circle.

Best regards
Manel