Assuming you have an accurate dial caliper, your filament diam. is quite high... ?!
Indeed, according to your measurements, you should over-extrude.
But, you don't, so something is wrong, just try with 2.85mm and see what happens.
Did you ever changed some steps per E, or density values (should be 1300 ) ?
If so, i should re-install Cura and change to 2.85mm filament diam. and see what happens...
About the gap between your bowden - filament, from what i've seen on many photos this is normal.
Assuming you don't have a faulty / cracked / torn bowden-tube, I don't believe this can cause a problem.
I assume you did install the "blue taped side" of the bowden at the extruder end ?
That's important, because that end of the bowden-tube is widened on the inside, so the filament can enter the tube easily (funnel idea).
Also check if the extruder-tension/ spring properly tightened (but not too tight), about 3-5 turns tight.