Suspend is only as complicated as any other time you have multiple triggers that trigger on the same time. The important thing to remember is that triggered abilities (like "at the beginning of your upkeep remove a time counter from this card") don't just happen automatically. You decide what order they happen and can respond to them, and respond between triggers as well. For your specific questions:
1. As long as you resolve the trigger to remove the last time counter from
Complete the Circuit first, you'll then get a trigger to cast it.
Complete the Circuit gets cast before you've even resolved the trigger to remove the counter from the other spell, so, when you resolve that trigger, you'll get a trigger to cast that spell, and can cast it, which will put the delayed trigger from
Complete the Circuit on the stack allowing you to copy it. That whole interaction involves 5 separate triggers, so don't feel bad about being confused. I'm a little confused myself.
2. You can't cast a spell without legal targets, so
Insidious Will will remain exiled for the rest of the game. I spent a while trying to puzzle over a way you could get another spell on the stack while the "you may cast
Insidious Will without paying it's mana cost" trigger was on the stack, but they'll always resolve first. You can't respond to a trigger going onto the stack before it hits the stack, so counterspells just don't work ever with
suspend, as far as I can tell.
3. Technically,
Snap can be taken advantage of with instants, of course, and with abilities, and with the few effects that cause mana to stop emptying from mana pools, and even with cards that care about tapping and untapping, but, yes, in the vast majority of cases,
Snap's untap up to two lands clause is pretty useless off
suspend.