The "If this card is in your hand: You can Tribute 1 Dragon-Typemonster and 1 other Fiend-Type monster from your hand and/or your side of the field; Special Summon this card." effect is an Ignition Effect that is activated from your hand. (It does not target. Tributing 1 Dragon-Type monster and 1 other Fiend-Type monster from your hand and/or your side of the field is a cost to activate this effect. You can also Tribute face-down Defense Position Dragon-Type and Fiend-Type monsters.)
Increasing the ATK of "D/D/D Dragon King Pendragon" and destroying 1 Spell/Trap Card are not considered to happen simultaneously. Increasing the ATK is mandatory, but destroying 1 Spell/Trap Card is optional.
When the effect of "D/D/D Dragon King Pendragon" resolves, you choose whether to destroy 1 Spell/Trap Card on the field or not. Therefore, the effect of "D/D/D Dragon King Pendragon" can be activated even if there are no Spell/Trap Cards on the field. (In this case, gaining 500 ATK is considered to be the last thing to happen.)
The "Once per turn: You can discard 1 card; this card gains 500 ATK, then you can destroy 1 Spell/Trap Card on the field. This ATK increase lasts until the end of this turn." effect can only be activated once per turn. If it is activated during your Main Phase 1, it cannot be activated during your Main Phase 2.