In case you do need root: on Fairphone open root can be activated from the developer settings, so it comes more or less pre-rooted (see e.g. this post).
Based on this, I’m assuming you used the ‘internal’ (or adopted) storage option. In this case the SD-card is shown as internal storage (and won’t show up separately in the system any more - exactly as you describe). The bit about ‘the phone only’ is quite literal: the SD-card will also not be readable on other devices. In addition, factory resetting the phone will also mean you lose (access to) the data stored on the adopted SD-card (the card is encrypted for security, a reset deletes the key required for decryption). Remember to regularly back up your data to an external device.