(section: 3 / paragraph: a / line: 2-4)
No, supervisors do not have to ensure there is a valid entry for each letter/category combination. Yes, a grid may be created where one cell doesn't have a known valid answer.
(section: 3 / paragraph: b / line: 1)
It depends on how the category is phrased. If it does not specifically ask for scientific name then either are correct. Rule 3.g prevents students from using different forms of the same term apply. So if the letters in the grid were "f" and "i" the student would only get credit for either flu or influenza, but not both.
(section: 3 / paragraph: H / line: 1)
No, per section 3.h. "If the category asks for the name of a person, both the given (first) and surname (last) of a person must be written. Archimedes' full name is Archimedes of Syracuse and Galileo's full name is Galileo Galilei.
(section: 3 / paragraph: i / line: 4-5)
It depends on the description of the category. If the category was "name of element" then the atomic symbol could not be used. If it was "nuclear (atomic) symbol" then the name could not be used. However, if the category was "element" or "chemical element" the student could use either the name of the element or the nuclear (atomic) symbol. Please note that if the category was "name of chemical compound" and the letters were "N" and "S" the student could not use "NaCl" and "sodium chloride" as both terms are different forms for the same substance. (rule 3.g)
(section: 3 / paragraph: N/A / sub-paragraph: N/A / line: N/A )
It depends on the category description. If it said "Invasive Species" then either the common or scientific name would be acceptable. Please note if the answer has more than one word, the first letter of the 1st word is used (rule 3.f). Rule 3.g. also allows students to get credit for only one form of a response.