- No. Whether an increase in exchange rate will have a positive effect on stock price is a causal question that cannot be answered from the data alone. Under the Pearlian framework of causal inference, it is possible to establish causation without an experimental intervention if you can control for all confounders, but for financial variables like this, that is very, very hard. If, on the other hand, you meant to ask whether the conditional probability of observing an increase in stock price given an increase in exchange rate is greater than 0.5 (an observational question), you can in principle get that from the data but will need something more sophisticated than linear correlation (see below).
- Essentially, yes. However, there is also the possibility that there is simply low-frequency noise in the data that is independent of any variable you can measure.
Now, the larger issue may be that you are not using the right tools to analyze this kind of time series data, which is better modeled as a random process than random variable. You should look at the cross-correlation function to start. Also, if you want to establish "predictive causality" of exchange rate on stock price, you can look into Granger causality or transfer entropy. If you really want to quantify the probability of successful prediction, you will need to use a model that makes strong assumptions about the nature of the data-generating process.
However, the take-home message is that financial processes are very complex and difficult to predict. Even the predictions of top securities analysts on Wall Street often fail to do better than chance.