Can I connect memory sticks and external disks to my iPhone or iPad?
Yes, USB memory sticks, sometimes called flash drives, and external disk drives can be used with iPhones and iPads. iPhones and iPads have either Lightning or USB-C charging sockets and the majority of flash drives and external disks still use the older and larger rectangular USB-A plugs which only fit one way round. These cannot be inserted directly into either a Lightning or USB-C charging socket and an appropriate adapter will be required. Apple are slowly phasing out their own, proprietary Lightning connectors in favour of USB-C, which is an international standard. All current iPhones have lightning chargers but iPad models vary. Any adapter you purchase will fit into the charging socket and you must buy the correct Lightning or USB-C adapter. Lightning and USB-C plugs are very similar. Lightning plugs are completely flat while USB-C plugs have a hollow centre which you may be able to see or feel with a fingernail. If in doubt, get assistance before purchase.
I recommend buying Apple branded adapters. I've had problems with cheaper products from other manufacturers. For historical reasons the devices you will need are called camera adapters.
Apple sell two camera adapters for iPhones and iPads with lightning charging sockets. Apple's Lightning to USB Camera Adapter has a lightning plug at one end and a USB-A socket at the other. The Lightning to USB-3 Camera Adapter offers better speeds for flash drives and external disks with USB 3 connectivity.
To connect devices with USB-A plugs to iPads with a IBS-C charging socket you will need Apple's USB-C to USB Adapter.
As Steve Jobs used to say, there is just one more thing. Flash drives get their power from the device to which they are connected and many external disks do the same and don't come with a power lead of their own. I'm not sure of this but I believe that no iPhone or iPad with a lightning charging socket will supply sufficient power for a flash drive to operate. That's not a problem; you just need to acquire one more item, a powered USB hub. These can be purchased inexpensively online. I bought a hub with four powered sockets from Amazon for less than £20.
So, to connect your USB-A flash drive or external disk to an iPhone or iPad with a Lightning charging socket, you will need one of Apple's USB Camera Adapters and a powered USB hub that you will plug in to the Camaera Adapter. You can then plug the flash drive or external disk in to one of the sockets of the powered hub.
The Files app will spot the flash drive or external disk and will give you full access to its contents. There are some restrictions to how the external device should be formatted but these are unlikely to pose a problem.
If you have an iPad with a USB-C charging socket you will need to purchase Apple's USB-C to USB adapter if you wish to connect USB -A flash drives or external disks to your iPad. You probably won't need a powered hubn. If your flash drive or external disk has a USB-C plug then it may be connected directly to the iPad and no adapter or hub will be required.
Finally, here's a link to Apple's information on connecting external devices.