A: Can we get banned from search engines for promoting multiple domains?

The answer is yes and, well... no.

Yes it can be a bad thing to promote multiple domains via search engines, but it depends on whether each individual domain contains identical or unique content. Having a look at the domains listed in your email, it seems that each contains links to the exact same content.

I understand the need to use different domains for marketing and advertising purposes, but what you should be doing is hosting all these extra domains on the same IP address so they resolve to a single site. Most site hosting firms offer this under the term "Parked Domains", meaning when you type in those domains in a browser, they automatically resolve to your main domain. Parking the domains on the same IP should prevent the search engines from indexing multiple sites and penalizing you for trying to sp@m them using duplicate content.

Forget the idea of your site being banned from search engines though. From what I understand, this is highly unlikely and only happens in extremely blatant cases of search engine abuse.