Does Adobe Lightroom store metadata in the pictures? Which metadata is actually stored in which isn't?
Lightroom stores all of its metadata in a SQLite3 database file found in the folder
LR will read metadata from the source image file when importing the image, and store it in the database.
On request, it can copy much of its metadata back to the source image file. This is occasionally required if the source image is used as input to another imaging tool so that all of the data captured by LR is available.
When writing metadata back to a source file, LR will often place the new metadata in an XMP sidecar file. The algorithm it uses to decide between a sidecar and (losslessly) updating the original actual file are obscure, and not well documented. In general, if its XMP implementation is confident of its ability to safely modify the original (which is true of .JPG and .DNG among other formats) then it will always modify the original file. Otherwise it usually makes a sidecar instead. If it does update the original file, they promise that the only changes are to the metadata, and not to the image itself.
The excellent and handy utility ExifTool can be useful to identify what metadata is actually present in any image file.
This article should help: Making Sense of Metadata Settings in Lightroom.
In general, all good (photography) image file handling programs will retain the original settings right up to the file timestamp intact and work with copies, registry or sidecar files.
When the original might be touched it will usually be preceded with clear indications of that action.
To store the metadata inside the file you can:
(Tested in Lightroom 3 beta)