Good answers. A few fine points:
To dictate, place one die you rolled next to your strip.
The die used for Dictate goes to the right of the phase strip, where the --> arrow points. The die being dictated is shifted to a different column. See the example diagrams on page 3 of the rules.
Now you may move another die you rolled below any column of the strip (not on the black spot) without changing its face, and treat it as that column's symbol when it comes to resolution of that phase. Do keep the die out by the strip until the dice are revealed, to show proof that you paid for dictate.
During the cleanup, you put the dictate die back in your cup. My group usually does this as soon as the dice are revealed for ease.
Actually, by the rules (see Reveal, page 4), this is done immediately after lifting screens, not during the Manage Empire (cleanup) step at the end of the round. So, your group's convention is the actual game rule.
This is the same as reassign, you can move a die for each reassignment under any column while keeping the die's face.
Except that no die is placed in the Dictate area. That's the advantage of Reassign powers; you get to shift dice around as indicated without having to delay a die until the next round.
It is treated as the column's symbol during phase resolution. Usually with reassign, you are limited to what columns and/or dice you can move around. Note that this never applies to the die you place on the strip on one of the black spaces, those dice are indeed treated as their column's symbol but are not considered reassigned...that is [effectively] a free reassign effect each turn.
For losing dice, unless explicit on the card, lose from anywhere.