4.13: The word translated "died" here (NRSV) is literally "falling asleep" (koimao-mai) in the present tense. This is the same langauge Paul uses in 1 Corinthians 15 or Jesus in John 11 (Lazarus).
4:14: The clause "We believe that Jesus died" (NIV) or "For since we believe..." (NRSV) is a classic case of Greek using an "ei" clause with an indicative to indicate "Since A, then B."
The word for "bring" is "ag-oo" which also means "lead" (as in demagogue).
4:15 The word coming (parousia) just meant coming, but could also have connotations of a royal leader, a general say, returing to celebrate victory.
4:16 The word for command (keleusma) has military connotations (it can also refer though to the one who leads the rowers!). See http://www.paulandgreece.com/thessa/arch.htm for more on the military implications here.
4:17 The word here for sieze (harpaz-oo) is the same as in Philippians (He did not regard equality with God as something to be grasped; or He did not regard grasping as worthy of God.) Again, this is a word that has aggressive, if not military connotations.