Regarding data types as a general rule we recommend:
Category: suitable for anything that you want to put as a filter: PM Domain name, Bedrooms, Zipcode etc.
Quantity: better for numerical values that you will want to make operations (average, min/max etc.) on ex. review score. You can not make it a filter with this data type.
For any dates in the Calendar / Listing nights tables: You don't have to change the data model here. even with no type set, Metabase knows it is a Date. When creating a filter, just select "Time --> Date Range" instead of the usual "Other category", see example below: