Users can enter any data if you uncheck the checkbox from the "Error Alert" tab: "Show error alert after invalid data is entered". Also, you can leave this checked, but you can set the error alert style to "Warning" or "Information" instead of "Stop", this will allow invalid data.
As for the other request, excel will autocomplete a cell (does not matter if it is a cell with data validation or not) if it finds similar data on the same column, but with no blank rows between data. But, if there are more than one entries starting with the same text, excel will show an autocomplete entry only when you pass the common text: for example, if you have:
"invalid number" and


"invalid date",
excel will give you an autocomplete entry only after you type "invalid d", or "invalid n"; this means that if the entries are not unique, excel will not show you autocomplete entries...
There is a workaround to view in the list only the entries that match what you type, but it's not a real autocomplete, you have to type something, then open the data validation list: http://www.ozgrid.com/Excel/autocomplete-validation.htm