Golgari Keyrune, Time to Feed

[AwaySinceMirage]

If I tap {Golgari Keyrune} for mana, and then use that mana toward promoting it to a creature, it is of course a tapped creature, nearly worthless.
But a tapped creature can still fight using {Time to Feed}, is that correct?
And then, fight damage still counts toward Deathtouch just as well as combat damage, is that also correct?
And the opponent's {Boros Battleshaper} can't do anything about it, because he only cares about combat, and I can do this all in pre-combat main phase, correct also?
In short, can I cast Time to Feed, targeting his Boros Battleshaper and my (tapped for mana) Golgari Keyrune, and kill his creature? (looks like mine would die too)
Did that whole thing work?

Addendum: Thank you Noblellama for the answer below! Yes on my turn. Battleshaper was about to kill my other creature by forcing it to attack.