I have had my page for a while, but still find aspects confusing. Because my "likes" show up on my personal page and my business page. I tend to switch to my business page before I comment on other business pages because it will show my business avatar, not my personal avatar.
Also, I think if you add a page to your favorites, you can interact with that page from your business page. Try this by going to a different page of which you are a fan. On the lower left corner there is a link for "add to page favorite" or something similar.