1)
What are the connotations of "Go'el ha'Dam es ha'Rotze'ach"?
1.
Makos, 12b: It means that the Go'el ha'Dam is fully entitled to kill him - and anybody else who kills him is Patur. 1
1
See Torah Temimah, note 60.
2)
What are the connotations of "Ein lo Dam"?
1.
Rashi: It means that if the Go'el ha'Dam kills the murderer outside his Ir Miklat, it is akin to killing a dead man - who has no blood.
2.
Targum Yonasan: It means that if the Go'el ha'Dam kills the murderer outside his Ir Miklat, he is not guilty of murder.