If I have Peten the Dark Clown on the field and my opponent summons Zaborg the Thunder Monarch and I activate Bottomless Trap Hole. When my Peten the Dark Clown goes to the Graveyard did I now miss the timing of his effect because I used Bottomless Trap Hole?

Not at all. When "Zaborg the Thunder Monarch" is successfully Tribute Summoned, its effect is automatically placed into Chain Link 1. Then, when you activate "Bottomless Trap Hole", it is placed into Chain Link 2.

As you know, chains resolve backwards (the last card activated is the first to resolve). Assuming that no other effects are activated, here's how the chain would resolve:

Chain Link 2 resolution: "Bottomless Trap Hole" resolves; "Zaborg the Thunder Monarch" is destroyed and removed from play.

Chain Link 1 resolution: "Zaborg the Thunder Monarch"'s effect resolves; "Peten the Dark Clown" is destroyed.

As the last thing to resolve is Peten's destruction, you do not miss the timing for its effect, so you can certainly activate its effect in this scenario.

What if I was to chain Torrential Tribute instead of Bottomless Trap Hole. I am assuming that Zaborg the Thunder Monarchs Chain Link Effect still needs to resolve even though he is not there and the effect just disappears. Since Peten the Dark Clown goes would then go to the graveyard during chain link 2 would I still be able to remove himself for his effect?

Even though Peten the Dark Clown is destroyed by Torrential Tribute, it is not the last thing to occur. When his effect Trigger's, the chain link formed by Zaborg the Thunder Monarch and Torrential Tribute has not yet "fully" resolved.

Zaborg the Thunder Monarch must still resolve his effect, even though it will be unsuccessful, as his target is already destroyed and removed from the field.

Peten misses the timing.