How can I get date and time formats based on Culture Info?

You can retrieve the format strings from the CultureInfo DateTimeFormat property, which is a DateTimeFormatInfo instance. This in turn has properties like ShortDatePattern and ShortTimePattern, containing the format strings:

CultureInfo us = new CultureInfo("en-US");
string shortUsDateFormatString = us.DateTimeFormat.ShortDatePattern;
string shortUsTimeFormatString = us.DateTimeFormat.ShortTimePattern;

CultureInfo uk = new CultureInfo("en-GB");
string shortUkDateFormatString = uk.DateTimeFormat.ShortDatePattern;
string shortUkTimeFormatString = uk.DateTimeFormat.ShortTimePattern;

If you simply want to format the date/time using the CultureInfo, pass it in as your IFormatter when converting the DateTime to a string, using the ToString method:

string us = myDate.ToString(new CultureInfo("en-US"));
string uk = myDate.ToString(new CultureInfo("en-GB"));