interaction and random slope

I am in my infancy role as a statistician. I have some questions regarding fitting a mixed effect model.

I have some repeated measures data: specifically I have 60 countries, each have 20 years of follow up (1990 to 2010) of annual measure of mortality rate (which is the response variable and let call this U5MR) and other repeated measures of variables such as the yearly population size, the average personal income for that year (call this PI), the percentage of women who can read and write (i.e. literacy rate).

But I will just use the variables U5MR, PI and time (time is the number of year from 1990 , so it is 1, 2, 3, 4, ... all the way to 20).

I am thinking of fitting a mixed model with random intercept and random slope since I think each country has a different baseline of U5MR (i.e. at 1990), and also it seems that the trend of U5MR when plotted against time (i.e. the time from 1990 to 2015, in my case it is 1, 2, 3, 4, ... 15 as a continuous variable).

My main question is:

Do I need to add an interaction term for say time*PI or random slope actually already take care of the interaction between time and the variable PI (i.e. average personal income)?

I am little bit confused about the difference between interaction and random slope. I know that random slope means that there is different of trend or different of slope for different cluster (in this case, it is the country). But I thought adding the interaction term also means there is difference of slope.

So my question is: when I have random slope in a model, does it already take care of interaction between say the variable Personal income and time?

In general, if I have included a random slope in my model, do I still have to include any interaction term in the model?

Anyone could explain more about the relationship or difference between interaction and random slope would be great.

Thank you.