I have a hosting account and add multiple domains to it, Is the contents of one site/domain affect the others?
not sure but i would presume that each of your domains on the same account will be add-on domains using the same IP unless you specify a unique IP for each of those domains. So, if they all use the same IP and SMTP gets blacklisted by several providers, then yes, you will experience the same results for other sites. I would recommend using a unique IP for each site.
Whether (or how) the contents of one site/domain affect the others will depend upon how your hosting plan enables you to use multiple domains
If you're wanting to avoid SMTP blacklist problems caused by other users of the same mailserver, I would suggest considering a VPS if it's within your budget - this will give you your own private SMTP server and therefore any blacklisting issues could only arise from problems with your site(s).
In terms of the sites/content being banned somewhere by some provider or organisation etc. I would guess that this is typically done via domain name rather than IP and therefore other domains pointing to the same content would need to be targetted individually (and domains pointing to different content would presumably avoid being blocked)