Universal Turing Machines in "Computational Complexity" by Papadimitriou
In response to your second question, you are correct -- a 2-state, 3-symbol state TM was shown to be universal by then-undergraduate Alex Smith in 2007 by reduction to a universal cyclic tag system, which makes for a complex encoding.  Here's the original proof, which uses Wolfram's nonstandard notation for representing Turing Machines.

It's easy to intuit why simpler universal Turing Machines require more complicated encodings -- after all, the information involved in the computation needs to go somewhere.  For example, in the encoding scheme implicit in Smith's proof, we would first need to first encode the Turing Machine under simulation within a cyclic tag system, then use Smith's scheme to represent the cyclic tag system within the 2-3 Turing Machine.