NRI & Aadhaar

Yes. An NRI (whether minor or adult) with a valid Indian Passport can apply for Aadhaar from any Aadhaar Enrolment Centre. In case of NRIs the residential condition of 182 days is not mandatory.

If your passport has the name of your spouse, then it can be used as Proof of Address for them.

NRI can act as HOF in the capacity of mother/father/legal guardian for Aadhaar enrolment, by submitting valid proof of relation (POR) document. List valid supporting documents is available at List of Supporting Document

An NRI child seeking enrolment to visit an Aadhar enrolment centre along with Mother and/or Father or Legal guardian and submit a request in requisite enrolment form alongwith valid supporting documents. Enrolment and Update form can also be downloaded from https://uidai.gov.in/en/my-aadhaar/downloads/enrolment-and-update-forms.html

The enrolment operator shall capture the following informations during the course of enrolment:
Mandatory Demographic information (Name, Date of Birth, Gender, Address and email)
Optional demographic information (mobile number )
Details (Aadhaar number) of Mother and/or Father or Legal Guardian (in case of HOF based enrolment) is captured . Both or One of the parents/ guardian has to authenticate on behalf of the child and also give consent for enrolment of the minor by signing the enrolment form.
And
Biometric Information (Photo of child)
Type of documents presented [valid Indian passport of the child is mandatory as Proof of Identity (PoI)]
Residential Status ( Resided in India for at least 182 days is not applicable for NRI)
After completing the enrolment the operator shall return all the documents alongwith an acknowledgement slip containing the applicable charges (New Enrolment is Free of charge).
List of valid supporting documents is available at List of Supporting Document

You can locate the nearest enrolment centre at : Bhuvan Aadhaar Portal

Yes, however messages shall not be delivered on international/ non-Indian mobile numbers.

The process is:
An NRI seeking enrolment to visit an Aadhaar enrolment center and submit a requisite form along with valid supporting documents. Enrolment and Update form can also be downloaded from (Enrolment & Update Forms) 

The enrolment operator shall capture the following information during the course of enrolment:

Mandatory Demographic information (Name, Date of Birth, Gender, Address and email)
Optional demographic information (mobile number)
And
Biometric Information (Photo, 10 finger prints, both Iris)
Type of documents presented [valid Indian passport is mandatory as Proof of Identity (PoI)]
Residential Status ( Resided in India for at least 182 days is not applicable for NRI)

After completing the enrolment the operator shall return all the documents along with an acknowledgement slip containing the applicable charges.
List of valid supporting documents is available at (List Of Supporting Documents)  
You can locate the nearest enrolment centre at : (Bhuvan Aadhaar Portal)

Yes. A valid Indian Passport is mandatory as a Proof of Identity (PoI) for NRI applicants. You may choose to give any other Indian Address with a valid supporting Proof of Address (PoA) as per the list of documents acceptable by UIDAI:List of Supporting Document

NRI seeking enrolment need to visit an Aadhar enrolment centre and submit a request in requisite enrolment form alongwith valid supporting documents. Enrolment and Update form can also be downloaded from https://uidai.gov.in/en/my-aadhaar/downloads/enrolment-and-update-forms.html
The enrolment operator shall capture the following informations during the course of enrolment:

Mandatory Demographic information (Name, Date of Birth, Gender, Address and email)
Optional demographic information (mobile number)
And
Biometric Information (Photo, 10 finger prints, both Iris)
Type of documents presented [valid Indian passport is mandatory as Proof of Identity (PoI)]
Residential Status ( Resided in India for at least 182 days is not applicable for NRI)
In case the NRI requires an address other than that mentioned in passport, he has option to submit any valid proof of address document available to resident Indian.

After completing the enrolment the operator shall return all the documents alongwith an achnowledgement slip containing the applicable charges.
List of valid supporting documents is available at List of Supporting Document
You can locate the nearest enrolment centre at : Bhuvan Aadhaar Portal