The relationship between rates, inflation, purchasing power and exchange rates...

I am a bit thrown off by the relationships between inflation, rates, currency appreciation/depreciation and exchange rates. I have put together the following statements and I was wondering if they were correct? If anyone could add any pertinent/useful information to them, that would be great. Thank you in advance.

If inflation in country X increases vs. country Y, currency in country X will appreciate relative to country Y. There is an inverse relationship between exchange rates and interest rates in two different countries. If inflation in country X increases, the purchasing power of that currency domestically will decrease in real terms.

An interest rate decrease will increase aggregate demand which over time will increase inflation.

A decrease in real rates causes currency to depreciate in foreign markets, and domestic exports to increase.

1) Statement in Question :If inflation in country X increases vs. country Y, currency in country X will appreciate relative to country Y. There is an inverse relationship between exchange rates and interest rates in two different countries. Analysis :The above statement is false. Inflation in a country leads to depreciation in its currency. This is because if the price levels in a country and hence inflation goes up, then the consumers will increase their purchase of relatively cheap foreign goods, thus leading to a depreciation in its currency. Hence the above statement in question is flawed and hence if inflation in a country X increases vs country Y, currency in country X will depreciate wrt country Y. 2) Statement in Question - If inflation in country X increases, the purchasing power of that currency domestically will decrease in real terms. Analysis: The above statement is true in all respects. This is because if inflation in a country X increases, then the amount of goods that can be purchased with say 1$ will now be bought with say 1.02$. Hence the purchasing power decreases domestically. 3)Statement in Question: An interest rate decrease will increase aggregate demand which over time will increase inflation. Analysis: The above statement is true. Generally as interest rates are lowered, more people are able to borrow more money. The result is that consumers have more money to spend, causing the economy to grow and inflation to increase. Likewise, opposite holds true for rising interest rates. As interest rates are increased, consumers tend to have less money to spend. With less spending, the economy slows and inflation decreases. 4) Statement in question: A decrease in real rates causes currency to depreciate in foreign markets, and domestic exports to increase. Analysis: A decrease in real rates causes inflation, leading to a depreciation in its currency. If the currency depreciates, it stimulates domestic exports and makes imports more expensive.This can be illustrated with the help of following eg: Consider a garment exporter in India whose primary market is the US. A shirt that the exporter sells for $10 in the U.S. market would fetch her 500 rupees when the export proceeds are received (again ignoring shipping and other costs), assuming an exchange rate of 50 rupees to the dollar. But if the rupee weakens to 55 versus the dollar, to receive the same amount of rupees (500), the exporter can now sell the shirt for $9.09. The 10% depreciation in the rupee versus the dollar has therefore improved the Indian exporter’s competitiveness in the U.S. market.