The overarching theme here seems to be the number 4, and with this in mind, looking carefully at the grid reveals we've been presented with a series of examples of the
Four Fours game. Going either vertically down a column or horizontally along a row, the mathematical operators distinctly segregate sets of four 4's (they The fact the 4's in the grid are greyed out implies we might want to write over them, but it's not exactly clear what should be written on them yet. For instance, we might try writing "234" or "0234" over the top of the first column, but after working out few more Four Fours solutions, it turns out these numbers can't possibly be written in without clashing digits.
The key step here is to look back to the theme and realise that a more suitable system would be to enter the derived numbers in (Note this can also be used to confirm what the operations and their ordering is. In particular, the dot before a 4 represented .4, or 4/10, while the dot-plus-bar represented .4 recurring, or 4/9). We now have a grid that contains only the numbers 0 through 3, and has lightly coloured edges with heavily marked corners. All signs point towards this being a Slitherlink puzzle, one of the better known Japanese box/Nikoli puzzles. It's clear this Slitherlink is slightly unconventional in that it can't possibly contain only one closed loop, but if we approach it assuming that it contains a set of distinct, disjoint closed loops, the grid is uniquely solvable:
Finally we want to extract the answer. The loops seem to spell out the message
It turns out this level is named |

The answer is: thesnake |
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