I couldn't live without my desktop machine, but in the Apple world the magic word appears to be "Airprint," a WiFi connection. Some printers have it, that's important to look for. There is also another way to connect, but you need at least a small cheap computer for a spooler. There's an app called PrinterPro which can be installed on a Windows desktop and on the iPhone or iPad, which shows up as a printer which various other apps can send to for printing. In general, as an olde DOS/Windoze guy, I find some of the iPad/iPhone stuff a bit frustrating, especially in regard to file management issues, but I guess with patience it can be done. I have the apps, because my wireless Canon color inkjet does not have the Airprint interface, but haven't really used them much beyond ascertaining that they work.
I honestly don't know if the phone or iPad can talk to the scanner -- my color machine is an all-in-one (Canon MG6300) and I have an iPhone 6s and an iPad Air 2, but have never even thought to try. Don't know if any of the all-in-ones use BlueTooth, but those sorts of specs are changing faster than my aging brain can keep up with!