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Hello @deep !
The first of all, the full-featured nested forms will require to have the custom module.
Let's review your questions:
1) Yes, it's correct, you should have the table which will store your form data.
2) Yes, you should have the PHP code which will process your data and show the next form according to the entered info.
3) Such custom check is possible to do in the code, but commonly the date fields are validated for the proper format.
4) The forms have the "view" mode like we have for the Persons Info.
5) It could be corrected by the CSS editing in the Custom Styles. It needs to work with the
.bx-form-row-view-caption and .bx-form-row-view-caption CSS classes.