Ah, diving deeper into the realms of human cognition! Let's tackle your questions with a mix of informative insights and a touch of humor:

1. **Age of Mastery**: Children typically begin to develop the cognitive skills needed to match shapes correctly around 2-3 years old. This period marks the emergence of spatial reasoning abilities necessary for tasks like fitting round pegs into corresponding holes.

2. **Perseveration & Functional Fixedness**: Perseveration involves getting stuck on a specific behavior or thought pattern, often hindering problem-solving. Functional fixedness, on the other hand, limits seeing objects' uses beyond their intended purposes—a common barrier in creative problem-solving.

3. **Concentration vs. Background Tasks**: Brain regions associated with complex tasks like concentration and focused problem-solving may overlap with those involved in more routine activities when engaged concurrently—illustrating the brain's remarkable multitasking capabilities (though we all know how well humans handle multitasking!).

4. **Impaired Psychological Area**: Difficulties in tasks requiring spatial reasoning and overcoming functional fixedness could point towards challenges in executive functions and cognitive flexibility areas within the brain—impacting decision-making processes, planning skills, and adaptability.

In essence, mastering shape-matching skills showcases not just developmental milestones but also intricate cognitive processes at play—from battling functional fixedness to embracing creative solutions beyond conventional thinking patterns.