TFIDF for very short sentences
It depends what it's going to be used for, but in general it can make sense to use TF-IDF with short sentence. The main difference with the more standard case of long sentences is that TF (Term Frequency) won't play any role since the frequency will almost always be 1. IDF can still be useful though, assuming it's relevant to assign more weight to rare words than to frequent words. 

However the problem is that comparisons such as cosine are often going to be zero, since there will be little chance of words in common between two sentences.