Would it be correct to use exchange rates of the biggest trading partners to the dollar as an explanatory variable? I'm trying to study the relationship of general macro factors and their effect on credit in the private sector. 

The country in question has a fixed exchange regime with the dollar, would it be correct to use exchange rates of the country's biggest trading partners to the dollar as an explanatory variable.

I'm not sure if should be regressing on the absolute figure of credit, or the year to year change in credit. My reasoning for the latter is that since I'll be using GDP growth rate, CPI based inflation, it's best to see how their changes effect changes in credit. If that's the case, should I use changes in oil price and the stock index, or their yearly averages?
When a variable is measured over a period of time, it is a flow variable.  When measured at a single point in time, it is a stock variable.  In your case, I think you are looking to explain the year/year change in credit, a flow.

Think about the case with the level of credit as the dependent variable.  Does one year GDP growth explain the overall level of credit in this economy?  Most likely not.

Try to be cautious here on how you interpret the regression coefficients.  For instance, if your coefficient on GDP is 1, you cannot argue that GDP growth is causing increased credit flows.  This is because this model likely suffers from endogeneity.

To make the case for causality, an important step is showing the reader that your model satisfies conditional independence.  That is, the variables on the right hand side of the regression are uncorrelated with the error term.

Otherwise, it's useful to disclose that an attempt at identification was not made, and that the coefficients are more are less statistical summaries of how the data move together.