1)Can I store a LR developed raw file outside of LR?
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Yes, at least 2 ways.
1) by exporting a file in the format of your choice, from less (TIFF, 16bits, ProPhotoRGB) to more compressed (JPEG). Readable in many, many apps as long as they understand the file format and color management.
2) by simply saving the metadata to the file (or having "autosave XMP" checked), it saves LR adjustments in the XMP space (sidecar file for raw formats). You can then copy & paste the raw file and its XMP sidecar together. This solution is lossless but works only in other Adobe apps (Photoshop CS3 with the latest version of CameraRaw, namely).
For the printing question, I'm not really sure to understand the question but anything is handled under the hood and no file output is apparent to the user. It's what Print Module is made for .
For technical questions about the print pipeline, you'd better have someone more informed to answer you but for my 2c's I'd think the images are treated for output (resampling/sharpening) and then converted from internal color space (very close to ProPhotoRGB) to the specified printer color space and passed to the driver, with the bit depth according to the printer driver (8 bits in most if not any cases?).