'Corn' in this sense is British English for "grain, cereal", not maize.

I've recently wrapped up my dissertation on Caesar's two invasions of Britain, so perhaps I may be able to shed some light on this as I used his Gallic War commentaries as my main source.

Unfortunately I do not have the book on my at the moment, but I don't remember Caesar switching between first and third person. In the version I used, Caesar spoke exclusively in the third person.

As for grain, /u/talondearg sums it up nicely above. To add to this however, I can give an insight as to why Caesar kept sending out parties to forage for grain, though I'm not sure that is your main question.

Obviously an army of any size has to be fed, but to use the example of his 54 BC expedition to Britain, he had to feed 5 legions and 2000 Cavalry. That amount of grain that is needed is immense, Caesar cannot realistically take what he needs for say a 1 month invasion with him, as it would be too risky (what if his ships sink?) and also too much effort.

As such, Caesar in Gaul relied on the local land to supply his men with food. This is why there are so many references to his men going to collect grain in his commentaries.

You might find this interesting, but Caesar's second invasion of Britain (which was a complete failure by the expectations of Rome), was arguably halted due to the fact that the inland British tribes did not grow crops to eat, rather they ate meat and milk almost exclusively. Of course, there were other factors in why the invasion failed, but that Caesar couldn't even supply his army the further inland they went meant that he was always going to be limited to the coastal areas of Britain, regardless of other reasons why it failed.