This can be achieved in either ways , Accordion widget , javascript snippets or jQuery.
With Muse , you can add the form in accordion tabs which would display the "Type" where once user clicks on one type , that specific tab will open and form can be submitted, similarly for other types. You will not need any coding for this.
On BC end you can create the forms, but the page action that you are looking for would need a little tweak with code. It would be like 4 separate forms are each stored in divs, each visible through a tab (so it's all an accordion based scenario, except that tabs are replaced by checkmarks) . Basically on checking A, a certain form is displayed, while if B is checked, a different form is displayed, while Initially the A/B check is not part of a form, just a check/tab that activates/unhides the actual form, the respective value (a/b), can still be hardcoded in the form.
The codes are freely available on internet , you can search for js snippet to hide the contents if required.
For live chat team , login to admin section of your site then go to Help and support, the page will show you the options for chat.
Thanks,
Sanjit