Say I want to create a file. Then I was asked to enter the name. I want to use the date as the name of file. I want to use M-x insert date (I define myself) . How can I do that?
Set (or bind, depending on the context) variable enable-recursive-minibuffers to non-nil (e.g. t), before the first entry into the minibuffer.
That lets you use actions, such as M-x which themselves activate the minibuffer, from within a minibuffer. The second activation takes place in a recursive minibuffer. When it ends (e.g. you hit RET after replying to the M-x prompt), things continue as they were, with the initial minibuffer still active.