The struggle with the fluorescent pink might be due to the limitations of the DSLR. If it's only able to shoot 8bit colour, then the pink (and blues too) will be dampened due to this compression, even in raw. 10bit or higher can reproduce even more colour than 8bit and could possibly help(?) But this is just my guess!
I only recommend making prints yourself if you want the most control over your quality and color accuracy. That said, if the printer you are taking your drive/images to is archival, then you'll get a good quality print but you'll have to get test prints, then compare the colors to your painting, then go back and print again (repeat until the colors match). This is more work if you don't actually own the printer. Also, I can't imagine a library having an archival printer grade photo printer and letting the public use it. I think most art departments at universities have them, though, for student use. Watch to learn more about what an archival printer is for fine art prints and why its important to use one ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-bt3HLLTG-wc.html
Great question! You can work with a JPEG, the camera raw filter can still be used in Photoshop on a JPEG. You just open the file, and then select the camera filter from the filters drop down menu. All of the other tools I discussed in Photoshop can also be used on JPEGs
