Should a member of a national chess federation register himself separatef for FIN? I know a player that is already a registered player of a National Chess Federation (NCF). Is he required to register separately with FIDE to obtain a FIN?
According to [FIDE's rules,](http://www.fide.com/fide/handbook.html?id=180&amp;view=article] I'd say no

All NCFs are required to register their players with FIDE. The FIDE Regulations on Registration, Transfers and Eligibility shall apply. All players who already have a FIDE ID number before 1 January 2015 are considered to be registered.

But I've been asked by a FIDE arbiter to tell the player the procedure (and that he has to pay 25€ for that). The player I'm talking about has been registered already in the NCF for 2016 and 2017.
The section you quote from the FIDE handbook is very clear. It is the responsibility of the individual national chess federations to register their players. It is not the responsibility of the players. It is the responsibility of the national federations to pay the fee required by FIDE to FIDE.

That said some national federations will have more than one level of national federation membership for individuals. They will charge more for FIDE registered players than for non-registered FIDE players and recoup some or all of the FIDE registration fees that way.

Different federations handle this in different ways and it is nothing to do with FIDE. It might be helpful if you said which national federation you are talking about.

EDIT: Doing some research I see that you are Italian. The Italian chess federation (Federazione Scacchistica Italiana or FSI) has 3 levels of membership, junior (10 Euros), ordinary (25 Euros) and adult (42 Euros). You must be a member of the FSI to play chess in Italy organized by the FSI. Normally you join (and pay) for membership through your chess club. If you want to play in a congress but are not a member of the FSI (through a club or otherwise) then you have to pay the congress your FSI membership fee.

Note that the membership fees I have quoted are old and may be out of date.