Transferring an image from Pro Create into Adobe Illustrator -The image is appearing in poor quality

I have been asked to design a highly illustrated packaging box. I was given a PDF template of the box, which I am illustrating on top of using Procreate. I find Procreate a simple way of creating images, however once I transfer both a PNG and a PDF file (which is set in 300dpi and appears to be "high quality") onto Adobe Illustrator, the file is pixelated. 

I have used "Image Trace" and altered the settings of the paths and corners to vectorise the image but the outcome of this distorts the original image (both in shape and colour). I was wondering whether there was an alternative for this? 

Also, I was wondering whether there is a chance that I could connect my Ipad (and Apple Pencil) to my Mac so that I can use this as a graphics tablet? It would be really useful if I could draw using a my Apple Pencil straight onto Adobe software but I'm unsure whether this is possible. 

If this isn't possible, does anybody have any suggestions on software, devices or techniques which might help me?

Thank you in advance, Kate x