Alright, I will bite.
First, what is the advantage of a digital signal versus analog? Does digital get through where analog won't?
The D-Star codec is roughly 6 kHz in bandwidth where a normal FM signal is 12 kHz. This makes for less space in between repeater frequencies, which is one advantage. The short answer to the question of D-Star getting through where analog won't is, yes, it will. The long answer, however, is that it depends. If you are in an RF hole where nothing can get out, nothing, still, will get out. A good scenario we like to use is the "fringe of repeater communication" aspect. I am sure you have been on the fringe of a repeater coverage area before in analog. What generally happens is that your receive-ability fades into static until you are unreadable any longer. Because D-Star is based on a digital stream, your voice (or sometimes data) is assembled into a stream of bits and sent to the repeater for reassembly. This, in turn, will lead to (usually) a perfectly readable and full quieting signal until you absolutely are not readable any longer where your readability would have long gone into the static with analog. One caveat to this is that D-Star users experience something we affectionately refer to as "R2-D2". Sometimes the bit stream gets jumbled up, but the radio lets the audio pass anyway. What you get is audio that sounds like the Star Wars robot of the same name. Other than those rare occurrences, the audio is very clear during normal operations.
Second, can you go digital simplex? So far I've only seen and heard people using it with repeaters.
Absolutely. Simplex is not a problem at all. The only requirement when you are in digital mode is that both stations have D-Star radios.