The Notability app has the ability to record stylus, keyboard and microphone input. Widely used by university students for lecture notes.
The iOS operating system tends to prefer only a single app to run at a time, but it is possible that a mapping app, could be run in the background to record position information, perhaps something like GPS Runner. The data collected would have to be processed and synchronised later on the ground.
In theory a bespoke application could be written but not all of the system hardware is accessible to programmers outside of Apple approved developers due to proprietory software/hardware protection built into the operating system.