How to draw duplicate items in perfect proportions and equidistant from each other in Mandala drawings?
You need to start with a sketch frame and fill it in from there. You're not going to be able to freehand draw it (without a ton of practice).

Start with a circle, decide how many radials you want (in your last example there are 16) and then sketch them in using a protractor to get them even.

I'd start with two perpendicular lines, then do the 45 degree lines (that makes 8) and then split those in half every 22.5 degrees... that gets you the 16. Keep splitting them further in half if you want the sections smaller.

So, with 16, you'll have something like this (you could probably actually just use this image and trace it or work on a light table):



From there, sketch in a ring everywhere you want a main point to be, say every inch (~2.5 cm). There's no need for them to be equally spaced, though. You can always start with a smaller design 4-6 inch diameter and then add to it later.

Here's an example:



Once you have the frame, fill in one of the wedges (or two/three if you want the full mirror effect).

Once the wedge is done, mirror it for the wedge next door. Use the rings to keep the placement. At this point, it's just the matter of filling everything in properly. If you do it correctly, you should have a perfect mandala at the end.

It's going to end up being similar to the process of duplicating a photograph or drawing using a grid pattern and filling in the grid rather than trying to draw it from scratch. Here's an example: