Does C# have extension properties?
For example, can I add an extension property to DateTimeFormatInfo
called ShortDateLongTimeFormat
which would return ShortDatePattern + " " + LongTimePattern
?
No they do not exist in C# 3.0 and will not be added in 4.0. It's on the list of feature wants for C# so it may be added at a future date.
At this point the best you can do is GetXXX style extension methods.