If you go to General Settings > Search Services and edit the Universal Search service and change the Result URL value from: universalsearch/{0}?SmartSearch=true to: universalsearch?SmartSearch=true&Q={0} That will fix the 404 error when entering a "/" in the search field.
That said, universal search does not index any boolean, date, or number fields on a model, so you can't use it to search for birthdate.
To search for phone numbers, it requires you to NOT enter any special characters. So you would need to just enter the digits.
It is possible to add new search types to the dropdown though with code. So if they had to have a birthdate search, it could be done, although depending on their use-case might be better just to create a filterable report for that.