Thank you for the feedback, and though beat late here are the answers to your 2 questions:

1. For deciding the estimate of the variance for the two groups you need to perform what we call A/A Testing ( to compare two identical versions of a product or service to determine if there are any significant differences between them) and obtain the variances of each of the groups from your own current data.

2. Good question, and no it doesn't make a difference, when the sample size is large enough (>30 as a common threshold) we make use of the Central Limit Theorem which says that the sampling distribution converges in distribution to Normal distribution. Therefore as your sample is large both T-test and Z-test will produce similar results and you are entirely safe to then use the Z-test, this is also why I suggest to use the Z-test.