STBL-079
Tyrant's Temper (Tyrannical Coercion) - Continuous Trap
Tribute 1 monster. Face-up monsters you own are unaffected by the effects of other Trap Cards.

1. On "Dragon's Rage":
Will my dragons still have the "trample" effect?
---since it's focus is on the gameplay (event of attacking a def monster which has low defense). So I still have the "trample", right?

2. Cost:
Will I still have to offer my face-up monster as a cost for a trap (let's say Icarus Attack).
Or will it be a free Icarus Attack?

1.) Dragon's Rage does normally affect all your Dragon-Type monsters, so Tyrant's Coercion will prevent them from having trample while it's face-up on the field.

2.) Costs are NOT part of the effects. Costs are always separate and are done first just to activate the card in question, and cannot be negated. Only cards that specifically say that you do not have to pay costs are the only way to circumvent them (like Spell Economics for activated Magic Cards).