You can't use bump or birthday tool. Bump is for interacting with groups, pages can't interact with groups, birthday tool is for posting on walls of FB profiles, pages can't interact with profiles in that way.
You're able to use Comment&Like tools as your page to comment/like posts of other pages. Go to Comment&Like tool > Sources, add pages there, then you can check "Execute action as a page" and choose your page there for each added page in sources section.
You can also set one of your pages to be used for all pages in sources by using "Set page for all elements" option.