You can't edit RAW files or DNG files - they are both a type of RAW format - as such they are uneditable. None of the changes you make during conversion to an image will be saved in the file itself. However, any changes you make to the image at that stage of processing will be remembered by Adobe Camera RAW, but the changes don't actually take effect in the RAW or DNG files/data itself.
Yes it's true that a DNG will be slightly smaller than your camera's native RAW format, but you are only talking about a few megabytes difference per image.
You can certainly add lossy compression to a DNG file to make it even smaller, but then that defeats the purpose of archiving it. Much better to use the Adobe DNG converter and leave it set to the lossless compression default. Lossless compression will not affect the image quality whatsoever. "lossless" means exactly what it says - no loss of quality.
You can't use your image editing program to import a RAW, edit it at the pixel level, and then convert to DNG - it's not possible. Photoshop can't save or export DNGs, but Adobe Camera RAW can.
If you want to convert your RAWs to DNG for archival purposes, then it's best to convert the whole folder of RAW images at once to DNG. That is certainly the quickest method. Then open each DNG image as required in Photoshop, using Adobe Camera RAW, then edit it and save as JPEG or TIFF for printing.
Here's my own workflow - although others will have their own preferred method
1. Use the free Adobe DNG converter to convert all RAWs to DNG. It's really fast.
2. Open the DNGs in Photoshop (using Adobe Camera RAW).
3. Do initial processing in Adobe Camera RAW, and open the image in Photoshop
4. Do any pixel level editing in Photoshop
5. Save as TIFF (or JPEG) as required.
6. Print the TIFF.