Can I set the date to display the full month rather than the digit?

can I set the date selection so that we can choose between "January, February, March" and not between "01.02.03"?

It's not possible in the Date Picker field. You may consider using our Birth Date Picker widget:

https://widgets.jotform.com/widget/birthdate

or the localize calendar widget: https://widgets.jotform.com/widget/localized_calendar.

The same guide, https://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form.