The tweezers are called Smart Bombs. Once you have collected three or more of them, you can press and hold triangle to complete any puzzle. It takes one to two seconds for them to work, so try to use them when you hear the "ten seconds" warning. This will use three of the Smart Bombs, so if you ha five before, you'll have two left.
The blue clock/disk things are called Time Capsules. They bring the timer back to 30 seconds if it reaches zero.

Each Smart Bomb or Time Capsule you have remaining when you get to the very last puzzle in a bomb will add either 10 seconds or 30 seconds to the clock on that puzzle. If you're playing the story mode and have to pull out the colored handles, they add ten seconds each to the timer. In Arcade mode where you're playing Detonator Lasers, they add 30 seconds each.