Hereof, why did Miller shoot Dresden?
Miller killed him because he was going to get away with it. Watch the 3rd episode and you'll get your answer. ;)
Also, is Miller really dead? Miller is, naturally, presumed dead after the Eros incident but Thomas Jane's character appears to return towards the end of The Expanse season 3. After the Ring Gate forms near Uranus, a ghost of Miller starts speaking to Holden, prompting him where to go and what to do next.
Accordingly, why did Miller kill the scientist?
In "Static", after Miller went rogue and killed Dresden, the head scientist on Thoth, he is on the outs with the crew of the Roci. Miller may have killed him to avenge Julie, but he also did it out of a sense of duty to the belt.
Is Miller in Season 5 of the expanse?
The Expanse began airing on Syfy in 2015 before switching over to Amazon for season 4. While Miller's arc mostly wrapped up in season 4, Jane, however, is not done with The Expanse yet, as he has returned to the show in a creative role for season 5.