Choosing ARIMA Orders from ACF/PACF

After differencing a series once, you plot its ACF and PACF:

• ACF: significant spikes at lags 1 and 2, then nothing significant beyond lag 2.
• PACF: decays gradually (roughly exponential), with no sharp cutoff.

1. What model order does this pattern suggest, and why?
2. After fitting, the residual ACF still has a significant spike at lag 12 with no other significant lags, on monthly data. What does that tell you, and how would you extend the model?
3. Why is p and q selection from ACF/PACF treated as a starting point rather than the final answer in practice?