I'm not sure what your first question is asking? "Does the east and west degrees have to be equal?"
If you are referring to the maximum and minimum software limits, the answer is no, the angle values don't have to be equal.
If your machine is moving to the correct altitude and azimuth values when you manually input them, then I think we can narrow down the problem to just a few possibilities.
The first would be like you said, the latitude and longitude coordinates might be wrong. If the getlatlon site isn't working, you could try using a GPS if you have one.
I oftentimes use Google Earth to find latitude and longitude coordinates. If you go to Tools >> Options, you will even find an option to display the latitude and longitude values in decimal degrees under "Show Lat/Long". That way you don't have to convert them yourself. Then you can just travel to your house and read the displayed coordinates.
If you send me your address, I can double check it for you. For a location in Germany, you should have a latitude about +50 degrees and a longitude about +10 degrees. A common error is to accidentally use a negative value where you should have put a positive one.
Another possibility is that you have the time set incorrectly. Maybe go through the instructions again. http://www.cerebralmeltdown.com/setting-the-time-on-the-real-time-clock/
Double checking the calculated angles in another program can actually make things a lot more confusing because you can easily make a mistake when inputting your settings in that program as well. I do have this program PC based program here that you might be able to use. http://cerebralmeltdown.com/forum/index.php?topic=361.0
If you have a smart phone, you should be able to find applications for it that will display that altitude and azimuth of the sun. Since most smart phones have a built in GPS and should automatically have the correct time, it is less likely that you will accidently use the incorrect values.
A few more random thoughts...
You might try getting the sun tracking to work first. If that works, then heliostat mode should also work.
Have you tried resetting the Arduino after the beam has drifted to see if it ends up where it is supposed to be after the reset has finished?
Are you sure you have the machine aligned correctly? If you are reasonably certain you have everything else setup correctly, you can put the machine in sun tracking mode and then adjust the altitude and azimuth until it points at the sun.
Which Arduino are you using, the Uno or the Mega?
Those are my thoughts on the issue. Let us know how it goes.