Is the any way show carousel cards in hangouts chat and also input field inside card?
One way we can do with pure html and css but is the any way do with card json.
There is not a built-in way to show carousel cards in hangouts, and also no way to include an input field, as you can see in the official documentation.
But I guess you could try to emulate a carousel functionality by doing something on the following lines:
If you have a WidgetMarkup, this could include buttons (maybe an ImageButton, something like a navigation arrow) that will trig some action if you click on them. This action could update the data inside the widget, so that, for example, if it includes an image, it changes the URL of the image. These URLs would be properly stored, ordered and retrieved from any kind of database (maybe coming from a spreadsheet? Or using Properties Service?).