Campaign Hypothesis Testing: Is using chi-square test appropriate?

I’ve just gotten the results back from a marketing campaign that consisted of testing new men’s and women’s apparel creative (test creative) against business as usual men’s and women’s creative (control creative).

I want to test to see if the lift in response rate was significant between...

1. The Men’s Test Vs Control Creatives
2. The Women’s Test Vs Control Creatives
3. All Test vs All Control

This is what my data looks like:

Name              Pannel    Sample_Size  RR_Numerator   RR_Dominator Res_Rate 
Men’s In-Target     Test    236,119      1,345          236,119      0.57%
Men’s In-Target     Control 207,715      1,220          207,715      0.59%
Women’s In-Target   Test    364,966      3,915          364,966      1.07%
Women’s In-Target   Control 542,786      4,489          542,786      0.83%
Model Test          Test    601,123      5,538          601,123      0.92%
Business As Usual   Control 750,573      6,185          750,573      0.82%

My questions are:

1.Is the appropriate course of action / decision mechanism to test significance a Chi-Square test ?

2.Should I be adjusting for the unequal Test vs Control sample sizes?