Translation:Please give me a knife.
Does 刀 function as a singular noun without a measure word? I wrote "knives" because it didn't say 一刀 or 一个刀 (I don't know what the measure word would be) and was marked wrong
Measure words is required when there are numbers. The measure word of 刀 is 把.
There is no number in this sentence, so here 刀 is a general reference. "knives" is not a wrong answer (although in real life people usually won't ask for two or more knives).
Yes it does. 一刀 means to cut/chop something (once) with the knife e.g. 一刀砍下去 and it's really 一把刀, 一个 isn't accurate although sometimes 一个 is acceptable with other more specific measure words.
Here it's "a knife" singular. Before there was 谁要叉？ "forks" plural. What's the difference?
Actually there is no difference. You can report it.
Besides, you may want to say "谁要叉子" instead of "谁要叉". Again, the latter one comes from someone who is not really familiar with colloquial Chinese.