The common thought is search engines consider the sub domain as an entirely different website, but your sub domain may be your competition. If you are selling yellow widgets on example.com and you are selling widgets on affiliate.widgets.com, you are competing against yourself.
Many of the errors and warning you are getting may be affecting just the affiliate.example.com.
If you site at affiliate.mysite.com, search engines probably recognize the content in the iframe as belonging to the Affiliate Company's website.
I believe you can do the diagnostics here for separate sub domains. That may help your focus on your controllable content.