🔧 Fix frontend warnings and add diagnostic tools

Fix:
- Add type: module to package.json to eliminate ES module warning
- Create separate backend/frontend startup scripts
- Add system status check tool

New files:
- check_status.bat: Diagnose system status
- start_backend_only.bat: Start backend separately
- start_frontend_only.bat: Start frontend separately

🚀 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

check_status.bat

@@ -0,0 +1,87 @@
+@echo off
+title QQuiz - System Status Check
+
+echo.
+echo ========================================
+echo   QQuiz System Status Check
+echo ========================================
+echo.
+
+echo [1] Checking Python...
+python --version
+if %errorlevel% neq 0 (
+    echo ERROR: Python not found!
+) else (
+    echo OK
+)
+echo.
+
+echo [2] Checking Node.js...
+node --version
+if %errorlevel% neq 0 (
+    echo ERROR: Node.js not found!
+) else (
+    echo OK
+)
+echo.
+
+echo [3] Checking PostgreSQL...
+psql --version
+if %errorlevel% neq 0 (
+    echo WARNING: PostgreSQL command not found in PATH
+) else (
+    echo OK
+)
+echo.
+
+echo [4] Checking if backend is running...
+curl -s http://localhost:8000/health >nul 2>&1
+if %errorlevel% neq 0 (
+    echo ERROR: Backend is NOT running on port 8000
+    echo.
+    echo Backend must be started first!
+    echo Run the backend window manually:
+    echo   cd backend
+    echo   venv\Scripts\activate.bat
+    echo   uvicorn main:app --reload
+) else (
+    echo OK - Backend is running
+)
+echo.
+
+echo [5] Checking if frontend is running...
+curl -s http://localhost:3000 >nul 2>&1
+if %errorlevel% neq 0 (
+    echo WARNING: Frontend is NOT running on port 3000
+) else (
+    echo OK - Frontend is running
+)
+echo.
+
+echo [6] Checking ports...
+echo Checking port 8000 (Backend):
+netstat -ano | findstr :8000
+echo.
+echo Checking port 3000 (Frontend):
+netstat -ano | findstr :3000
+echo.
+
+echo [7] Checking .env configuration...
+if exist ".env" (
+    echo OK - .env file exists
+    findstr /C:"OPENAI_API_KEY=sk-" .env >nul
+    if %errorlevel% neq 0 (
+        echo WARNING: OPENAI_API_KEY may not be configured properly
+    ) else (
+        echo OK - API Key appears to be configured
+    )
+) else (
+    echo ERROR: .env file not found!
+)
+echo.
+
+echo ========================================
+echo   Diagnosis Complete
+echo ========================================
+echo.
+pause