Fix parentheses_checker.cpp: remove <bits/stdc++.h>, support multi-line input, add comments (#8760)

[prateekshukla0918]

This PR fixes and improves the parentheses_checker.cpp file as discussed in issue #8760.

Changes made:

• Replaced non-standard <bits/stdc++.h> with , ,
• Added descriptive comments for clarity
• Program now reads multiple lines until EOF
• Removed unused commented-out vector test code
• Improved input prompts for better usability
• Reformatted code consistently

Tested locally using g++ -std=c++17 — working as expected.

Closes #8760