[ENHANCEMENT]: Clean up QA parsing and utility functions in eduaid_web for better performance

### Feature and its Use Cases

Some parts of the app have repeated logic for QA parsing, shuffling, and API handling. This can be cleaned up by moving shared logic into utility files and reusing it across pages.

What to improve:

- Move common QA parsing and shuffle logic into a shared utility
- Reuse the same logic across pages like Output and Text_Input
- Clean up API usage to make it more consistent
- Add some basic accessibility improvements where needed

Why this matters:

- Reduces duplicate code
- Makes the codebase easier to maintain
- Improves overall performance and readability

### Additional Context

_No response_

### Code of Conduct

- [x] I have joined the [Discord server](https://discord.gg/hjUhu33uAn) and will post updates there
- [x] I have searched existing issues to avoid duplicates