for the timestamp you can use the Date request header. It's not
mandatory, but it should be used often.

For the timezone you can take the ip address of the request and then use
one of those services that map the ip address to the location. If the
timezone is not directly available you can get it from the longitude.

Weird requirements you have

RFC 2616 does not require or even suggest that requests should pass either
a timestamp or a timezone, so you can't normally get get this information
from the client. So the best you can do is log the time you receive the
request, which is trivial.

The following RFC 2616 headers should (if present) contain date information

                     | If-Modified-Since        ; Section 14.25
                     | If-Unmodified-Since      ; Section 14.28

To access these, you use

javax.servlet.http.HttpServletRequest
public long getDateHeader(java.lang.String name)

"Returns the value of the specified request header as a long value that
represents a Date object. Use this method with headers that contain dates,
such as If-Modified-Since.
The date is returned as the number of milliseconds since January 1, 1970
GMT. The header name is case insensitive.
If the request did not have a header of the specified name, this method
returns -1. If the header can't be converted to a date, the method throws
an IllegalArgumentException.
Parameters:
name - a String specifying the name of the header
Returns:
a long value representing the date specified in the header expressed as the
number of milliseconds since January 1, 1970 GMT, or -1 if the named
header was not included with the reqest
Throws:
java.lang.IllegalArgumentException - If the header value can't be converted
to a date"