Chi - Square Test for test of independence of variables in different treatment groups

Hello together,
I have a question concerning my bachelor thesis. It is the first time I am actually doing statistical analysis on my own and so recommendations are very welcome. I work with a huge dataset of N=30000 with 10 randomized treatments group (variable „Treatment“ going from 0 to 9) and now i want to conduct balance tests for two things:
  • Test if gender (dummy variable 0=“male“ und 1=“female“) is statistcally different in the different treatment groups. We have two categorical variable (nominal scale) and therefore, I looked at chi square and with a high p-value (0.6) I can say that the differences in male and female are not statistically significant. Is this correct or should I use something else rather than chi square?
  • Test if Zip-codes are nearly the same for all treatment groups. I have three-digit numbers for Zip codes. Is a chi square method again the best way to test if Zip codes differ statistically significant between these groups? Again we have two categorical variables and thus I would think so or what else could be good method to test it?
Kind regards and thanks in advance