Who was the first to show that there is a Universal Turing-Machine that uses a binary alphabet?
A large part of what is known goes unpublished, when it is considered trivial. What counts as trivial is, of course, different in different times and for different communities. For instance, we do not consider particularly interesting about binary numbers that they are as expressive as decimals, but that the machines that operate on binary representations are simpler. 

In his famous 1936 article, Turing is satisfied with the premise that the alphabet of the machine is finite, which leads me to believe that differences beyond that are considered trivial by him, for general purposes. 

He discusses the difference between machines with infinite and finite sets of symbols, and reaches the conclusion that using an infinite set of symbols would, at some point, make it impossible to concretely differentiate them from each other (which could be another way of illustrating the fact that real numbers can't be listed). He then states that the effect of this restriction is not very serious, because you can, at least to some extent, conveniently represent bigger alphabets by groups of symbols of smaller ones, considering that any effective computation can only use, in practice, what amounts to a finite number of symbols.

I suggest that you try to imagine how to simulate an $n$-symbol TM (I would start with $n=8$) on a two-symbol one. It is a good exercise.