for Q1 and Q2 - i would suggest use the segment, refer the link below for more details.

https://www.qualtrics.com/support/iq-directory/segments-tab/

for Q3 - using Quota you can do this, refer the link

https://www.qualtrics.com/support/survey-platform/survey-module/survey-tools/quotas/

thanks Imran

@Juan Torres : 

here are answers:

1. Yes, you can automate sending samples in Qualtrics.
2. Yes, sample updates can be automated using contact lists.
3. Use distribution options and quotas to survey a % of customers from different branches.