Good morning, everyone,

I am not very familiar with existing econometric methods, especially with survey data.
Please, I have survey data for a country with 1000 respondents. this survey was carried out in several countries on a T date. (cross-sectional data)
as part of my study I would like to
1) study the influence of a variable X on a variable Y. (X and Y are categorical variables (Yes or No). I therefore think that the simplest would be a probit model...
however,

2) I would also like to see if there are differences in the influence of X on outcome Y depending on the countries. In other words, is it that for a country i, the influence of X on Y is different compared to a country J?
For this reason I would like to study this difference within a set of countries that are grouped under a sub-regional set that includes 8 countries.
if there are differences (which I certainly think there are) I can explain it by cultural, economic or other factors specific to each country.

My question is what method should be used to do this?
8 countries is that enough? knowing that I have a total of 8000 individual observations ( from different countries!) and that for theoretical questions I would like to study only this sub-regional set.

is a random effect probit or logit fix effect appropriate? before verifying by an intuitive haussman test a probit or tobit is it suitable for the two-level analysis I want to do?

should countries must be grouped according to shared characteristics and a differential analysis be conducted ( it's not my first idea but wy not )?

Has anyone ever had to do this kind of analysis? Any leads to provide me with?
thank you for your answers