Maybe I am overthinking this. But which person should I use in the fellowship application? There are sections about the actual science, about the applicant, and about the exchange with the host institution. Is it ok to switch person according to the section? Or should I refer to myself as the "Researcher" as the templates use?
Optimally, you would check this with people in your field, in the best case somebody who has already written a Marie Curie Individual Fellowship proposal. In my area, the usage of "I" has become fairly standard for personal grant applications, to the extent that using "they" would be considered somewhat unusual. Using "we" for such grants is not recommended, as apparently some people want to see this as a sign of lacking independence. (I completely disagree with this assessment, but why take the risk?).
An option that was suggest to me when I wrote my (successful) MSC application was to make use of the chosen project acronym (which you have to choose anyway). Use sentences like:
- ACRONYM will solve (world hunger).
- ACRONYM will overcome (major problem) by using (fancy sounding technique).
In my experience allows you avoid most cases were you would otherwise want to use "I" or "We" during the scientific proposal part (often simply to allow for the flow of the text). You will be left with cases that specifically refer to the applicant, who you can refer to as you deem appropriate (see other answers).