The flux etc needs to be cleaned off for proper inspection.
Here is Lincoln Electric's basic video about visual weld inspection. It is aimed at Boy Scouts getting their welding merit badges.
I think the "welder" needs at least to spend a few days running beads flat and vertical and making pad welds on 10 mm material to achieve at least basic proficiency. Even then, I don't think he should be allowed to work on your job again.
I think the "expert welder" is going have to do a LOT of grinding or arc gouging to fix those welds. And probably cut out and replace some sections entirely.
Pages 32 thru 33 here discuss a minor case of one of the obvious deficiencies of those welds you are having to deal with.
Note the corrective action of cleaning the weld area.
The lack of cleanliness is NOT causing most of the problems however.
I envision the beam welding requiring be done in 3 different positions. Flat, vertical, and even overhead.
Here is a video showing some very good "vertical up" welding in process, and proper surface and edge preparation for 3/8"/~10 mm plate. Full penetration welds generally require some beveling or other edge preparation and multiple passes. They are NOT done by blasting thru the material in one pass.
Overlook the extremely uniform weld surface appearance. There is some leeway there.
Can you see how the weld completely fills the space between the plates, and fuses completely with each plate?
here is another series, from Lincoln electric. OK, but they spend too much time recording far away.
They are all using 7018 electrodes. As I recall the flux removal is much easier than 6011.
But notice the uniform bead, slightly convex, fusing with each side of