SEO and RSS questions

1. Does it help or hurt SEO to embed RSS feeds from other sites into my forum or cms?

2. Does it help or hurt SEO to syndicate my own RSS feed to another site I control? If it helps, does the second site need to be on separate hosting or on a separate ip address?

You should avoid copying others' content by any means. If it is a valid resource to your membership, make that area members only so bots don't see it. Otherwise, you may face duplicate content penalties.