Suppose monetary policy becomes restrictive in the United States as a result of inflation fears

One realises that similar steps were taken by Mexico in the 80s-90s and it did not turn out well for Mexico:

Pegging the peso to the dollar in the face of large, sudden capital inflows and outflows presents mexico with the difficult task of trying to control teh fluctuations in peso/dollar exchange rate and maintaining a domestic growth rate that is not inflation heightened.

When faced with any sort of external shocks, the Mexican government would have to undertake large money market opertions and spend it's reserves.

b) Speculation would not really help Mexico stabilise , if anything it will lead to large amount of peso assets being turned over to dollar assets. This is down to the investors realising the only way Mexico has to maintain it's currency exchange rate is to undergo large money market operations