I have 6 options for my form, one of them is “Other”. When the user clicks on the option “Other”, the button should convert into the textbox and the user should be able to enter answer, which will eventually be saved too.
That feature does not exist in Gravity Forms. There is an “Other” option with a radio button field, but the “Other” option remains selected and then a new text field shows up afterward. It would not work or look like your screenshot. To achieve something like that would have to be custom developed.