The 'wagging dog-tail' button indicated that you are intrested in the profile you are currently viewing and would like to set up a playdate between your pets.

You can navigate from any point with in the application to the previous page using the back button in your browser. The back button on your android mobile also serves the purpose.

You can make more than one selection for breeds as well as size. It mimics the default/native multi-select across different device types. Hold the 'Ctrl/Cmd' key to select multiple items in a non-touch devices.
Tap/click on the input field/options below the breed( or Size), now a new window will pop up on your screen with options, Click on as many choices as you like to select it and click on 'ok'. The input feild now shows the number of selections made.