Why isn't dich in dative?
The verb kosten puts both indirect and direct object into accusative case.
Sein Verhalten kostet (1) ihn (2) meinen Respekt.
1: ihn = indirect object in accusative case
2: meinen Respekt = dir. obj. in accus. case
"Die Partei kostet dich kein Geld" - shouldn't this be accepted, unless Partei means something different than Party?
What you say is correct. There is no reason the sentence could not be referring to a political party.
Das Fest kostet dich kein Geld?
Why wouldn't "Die Party ist kostenlos" work?