quick question.

if i flip monster gate by diamond dude's effect.... next main phase, can i just start dropping cards to special summon the first monster that can be normal summoned, or do i have to tribute a monster on the field?

thanks for the help!

Tributing is part of the cost of Monster Gate, so you would indeed "start dropping cards" to start doing Monster Gate's effect untill you hit an appropriate monster.

so just to be sure, i WOULD NOT have to tribute a monster on the field for monster gate if it was used with Diamond Dude's effect. correct?

That is correct. You do not need to pay the costs for any spell card that was put into your Graveyard by Diamond Dude's effect but if the card requires targetting, you will need to have legal targets for it.