You need to put the name of your knot at the top of the page.
Your justification needs to go in the justification box. It needs to include the image, plus words justifying the assertion. Your projection is not a "regular projection". You need to fix that. (done)
The picture of your knot seems to be missing. (fixed, but there is still a dead image link)
Dowker: You need to list the Dowker notation for your knot outside the collapsable box. You mention that you got the Dowker notation of your knot from the original projection—that's what we need to see. Your justification should be a picture of your knot with crossings labeled. Then these labels generate the notation. You do not have to go back again from the notation to the knot. (partially fixed, see below)
Tricolorability: You're confusing tricolorability and mod 5 labeling. Here we want to know if your knot can be colored three colors according to the rules we learned in the text. Also, your box is split in two—you need a > on the blank line in your justification. (partially fixed, see below)
Conway: you wrote down the wrong notation for your knot. Therefore, you picture is incorrect too. (done)
Signed planar graph: You should have a new "section" for this, just like the other concepts. Outside the justification box you should have a picture of the signed planar graph. Inside the justification box you should put the picture that you drew. (partially fixed, see below)
Bridge number: put the picture in the box too. Your understrands cannot cross each other. Also, you have a typo "there" should be "the" (partially fixed, see below)
Dowker notation: The notation should only consist of even numbers. See comments above. Your picture should be the original projection of the knot. Your text does not make sense. (partially fixed, see below)
Tricolorability: You have shown that this particular coloring does not work. How do we know that there is no valid coloring? You still have a split box, as mentioned above. (partially fixed, see below)
Signed planar graph: Your section should start with ++, not +. Call it a signed planar graph. (done)
Unknotting number: correct. Now add a few words of justification. (not fixed)
Genus: Your Seifert circles aren't correct. Your formula isn't correct (need parentheses). You need to justify why your computed genus is the minimal possible genus. (changed, but still not correct)
Jones: your justification should be a complete sentence. (not fixed)
Amphicheiral: a couple of typos (partially fixed, see below)
Bridge number: this is not a projection of your knot
Dowker: your picture is correct, but your notation does not match the numbering in your diagram.
Tricolorability: You've shown two incorrect colorings. How do we know that there isn't some valid coloring?
Amphicheiral: you don't need to mention that it has fewer than 15 crossings.