How to do a time series / panel data analysis with macroeconomic data in Stata?

Just to preface this, I have very little experience with applied econometrics, I only had to take one class where we actually did a little practical work but most of it was theoretical and not applied. Still I have to write an empirical paper for a class for which I should use stata. This is for an undergrad program so the methods probably don't have to be super advanced.

The question is pretty much whether a country being a member of a currency board has a significant influence on inflation. I already have the dataset for it too, a selection of a few dozen countries, years from 1960 to 2013, inflation rates, a dummy variable that is 1 if the country was member of a currency board at the time and 0 if it wasn't, and a few macroeconomic control variables, one of which logged.

I thought I could use an Ordinary Least Squares regression with fixed effects with the time series data. But I've never done any time series analysis and I'm not really sure how to get started here especially because it's not just one but multiple countries, so I have no clue what to do really. Maybe someone could help me with how to get started with this? How to properly analyse it with Stata? I'd really appreciate it.

A few other questions:
  • I don't have data for each year as it's often the case with economic data, e.g. one control variable for one country in year x may not be available or the inflation rate for a country from time y to time z was not included. Do I have to consider this especially or will it not be a significant problem?
  • How do I check the "robustness" (sorry if that's not the right choice of word) of the results? E.g. should I exclude outliers in the data e.g. very high inflation rates, or should I exclude whole countries with a high average rate to see how these outliers may influence the results in the original regression?
  • Inflation is not independent from time, e.g. in 1960 inflation was generally higher and more volatile than in 2012. I remember something about heteroscedasticity which might be a problem for the regression, also time could be correlated to the dummy variable currency board as well. Will this be a problem and if so how can I address it?
Thank you for taking the time to read this and I'd really appreciate any help.
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