To send a Friend invite, go to your Me or Feed tab in the app and tap on the Add Friends icon in the top right corner of your screen, it's an outline of a person with a plus sign symbol. You can then search the username of who you want to add as a friend. You also have the option to connect your contacts and Facebook account to Runkeeper to help you more easily find friends!
To remove a Friend, go to your Friends List, and select the friend you want to remove (the Friends List Icon looks like 3-bullet points right beside the Add Friends Icon). Once you have selected the friend you want to remove, click the "Friends" bubble, and that will bring up a "Remove Friend" prompt.