Translation:Teacher, I don't know this character.
Can I say, "我不知道这个字."? If not, what is the difference between "认识" and "知道"? In my quest for learning Chinese, I have almost always used the latter.
I have learned that 认识for people is and 知道for knowledge but I am not Chinese so I could be mistaken or duolingo simply has a awkward sentence
You are correct, but the difference between "认识" and "知道" in this context is subtle (generally they both mean you don't understand this character), so in my opinion "我不知道这个字" means generally the same thing here.
http://grammarist.com/spelling/recognize-vs-recognise/ British English lists an alternate spelling as recognise, but the main entry is recognize. North Americans (yes, that includes Canada) prefer the ize spelling, and this is accepted everywhere. However, outside North America some prefer the ise spelling and it is not incorrect. This spelling change goes across all derivatives including: recognizability, recognisability, recognizable, recognisable, recognizeably, recognisably, recognizer, and recogniser.
The ize/ise change is based in English being influenced by French, and every other language. The Greek words changed to Latin, which used a z, but the French spelled it with an s. Purists in England promote the original ize while others stick with convention, ise.
To my knowledge, in some Western culture people call their teachers "Sir" or "Mr. /Ms. /Mrs. Smith" This is not used in our culture, we almost always call them "老师" or "教授"(professor). Addressing your teachers/professors with their name, even "林先生"(Mr. Lin) may be considered impolite by some people.