The fact that you are not a national of an EU/EEA Member State or Switzerland does not mean that the regulation cannot apply to you. For some categories of persons, it is not necessary to be a Member State national in order to be covered by the coordination regulation. This is the case for stateless persons and refugees as well as for family members and survivors of the persons who are covered by the coordination regulation (see the keywords personal scope, refugee, stateless person, member of the family and survivor).

Moreover, the coordination regulation has been extended, by virtue of a separate regulation (Regulation 1231/2010), to all third-country nationals who legally reside in a Member State and whose situation is not confined in all respects within a single Member State. This extension, however, does not apply in relation to Denmark, Switzerland, Liechtenstein, Iceland and Norway (see the keyword third-country nationals).

Once the regulation applies to a person (see the keywords personal scope and third-country nationals), his/her nationality is of little relevance. It bears no influence on his/her legal position, unless in some clearly defined cases of minor importance. These relate, firstly, to the rules determining the legislation applicable, in particular the special rules for EU contract staff (who may opt to be subject to the legislation of the State of which they are nationals), and secondly, to the provisions of conventions on social security between the Member States in respect of which it is specified in an annex to the regulation (Annex II to Regulation 883/2004) that their application remains restricted to the persons covered by it (see question 19.1).
 

No, they are not, at least not on account of their non-contributory nature, that is to say on account of the fact that they are financed from taxation and not from social contributions. The material scope of the coordination regulation extends to both contributory and non-contributory benefits.

Note, however, that specific rules apply to certain non-contributory cash benefits, which are special in nature (see the keywords material scope, benefit, social assistance, contributory benefit and special non-contributory benefit).