Seemingly you have already tried to make a SVG file by tracing the image in Inkscape, but with no success.
A fix: Your 100 x 100 pixels image should be scaled to bigger size to make Inkscape believe the dots are rectangles. Scaling it in Photoshop or GIMP to 1000 x 1000 pixels with the "nearest neighbour" resampling does the job. Rectangles get ...
Personally I think tracing this image as vector graphic is a bit overkill.
If converted to a png file with a reasonable resolution (quick way: just take a screenshot of the zoomed in tiff image):
your pdf reader should not have problems displaying the image:
(including it as image will avoid all problems with all these "thin line enhancements" ...
I would try the following image trace options. You want to make sure your corners are set to 100%. The end result is about 41kb SVG.
I think it turns out pretty good.
You could also try Object -> Create Object Mosaic. You will have to mess around with the amount of tiles you use.
I was creating plots in R with ggplots and faced the same problem (circles into squires). The suggested solution did not work for me, but a very easy one that worked was to change the transparency of the dots (for example alpha=0.2). Afterwards, AI does not read circles as text anymore and they are shown correctly!
This solution is so fast and easy, that I ...
Draw a rectangle and shear it. Copy the same in front and move accordingly. (You will need some measurements if you want both horizontal and vertical segment widths equal.)
Round the corners wherever you need
Fill color/gradient/strokes according to requirements
This is somewhat non-destructive. You can alter things.
If your pattern (I mean your artwork) is non-transparent, I think you just need blending mode Normal only. Then you can add a solid color layer (#375459) and use it as a clipping mask. You should get what you need.
What you're doing wrong: I think the problem is just blend mode you've set.
You can also use Layer > Layer Style > Blending Options > ...
Here are two options for you.
Inkscape's connector tool is most useful if you want to constantly tweak the layout. It's a little bit buggy but normally yields handsome results. This tool doesn't work well with snapping enabled.
For more intricate designs use the node tool with snapping.
If the path is only slightly curved towards the end, and nobodies' life depends on it, you can of course draw a circle at the end of the path:
Draw the circle using cmd + shift while dragging and make sure its' center has snapped to the last node of the path. Enter the amount you want to trim as the W and H value of the circle.
Then, select the path and use ...