I have a simple question. Can one look for correlations between percentage and average ? For example, percentage of unemployment and average salary. Or shoul I use total numbers instead ? If I look for a relation between percentages and average I get significant correlation, but between totals data is not significant.
The biggest risk of looking at statistics of the aggregates is ecological fallacy (example here). Group-level aggregates do not necessarily are suitable for inferring individual-level characteristics. The most vivid example is the Simpson's paradox, which shows how you can get completely different results when looking at group-level vs individual-level data. If you only have the aggregated data, your results do not necessarily translate to the individuals.
I'd be really uncomfortable with a correlation between a(n average of) continuous variable and a percentage, because the percentage is bounded by $[0,100]$. So if the percentage is near these boundaries, the relation (i.e. correlation) between the two is bound to be non-linear. A more suitable way of associating one continuous and a categorical variable is, for example, through regression.