Can I calculate the correlation between categorical and quantitative data?

1) one correlation is between term (36 months or 60 months) and the other data is a continuous variable. I coded the term data as 0 for 36 months and 1 for 60 months and ran a correlation through R. Will the results be valid?

2) I have a continuous variable that looks like it must be categorical after i graphed it. Does this mean that I should change the way I treat the variable? Would a correlation with this variable still be valid?

3) When are confidence intervals for correlations useful?

Thanks for the help!