I`m glad to hear that most of the functionalities are implemented.
For the last requirement, I can suggest once a day is clicked, to take a reference to the DOM element, it can be done by attaching click handlers to all DOM elements used or showing a date. This can be done on the dataBound event using the class of the date container:
Then once the element is located in the DOM to place a DIV container under the date container. Then if another date is clicked, to remove the previous container and to add the new one. Depending on the scenario "insert" or "append" can be used. Please have in mind that this will require custom logic to determine how the element can be inserted and additional styles for positioning as well.
Also, I can recommend our Professional Service team, which can assist with implementing the desired feature: