REST API GET method - api

Question

According REST API design recomendations, getting user by id must be
GET /users/{id}
How will look getting user by unique phone number?
GET /users/phone/{number}
or
GET /users/?phone=xxxxxxxxxxx
or
GET /phones/{number}/users
or anything else?
Or for example getting last user comments with limitation:
/users/{id}/comments/limit/{limit}
or
/users/{id}/comments/?limit='xx'
There are constraints or recomendations in such cases?
Which HTTP method is better to send request for making some actions (for example SMS sending).

Answer 1

There are a lot of different aspects in your question, so I am picking some and hope the answer is somewhat helpful to you.
Generally speaking, a URI ist he unique identifier of a certain ressource. Further more, "good REST-API URIs" contain only nouns (to 'name' the resource), not verbs (what should be done with the resource). URI parameters may be used to parameterize the ressources representation, e.g. sorting or filtering.
In your example,
/users/{id}/?limit='xx'
would be a valid way to fetch a list of some sub-ressources (possibly the users comments), but here is nothing on the URI that refers to a specific property or sub-ressource (e.g. comments).
A more meaningful ressource URI would be
/useres/{id}/comments/?max=100&sort=asc
In this case, the first part (users/{id}/comments/) identifies the ressource, while the params are used to parameterize its representation. Proper URI's do not rely on URI params to uniquely identify ressources.
Filter criteria in the URI may be treated similiar. You could put them in parameters, but that may lead to problems with multiple and/or complex filters, e.g.
GET
/useres/?phone=1234&phonemode=startswith&name=foo&namemode=contains
One way to do this could be to create a filter (maybe just temporarily) and then retrieving the filtered information with a subsequent GET request like this:
POST /users/filter
name='mycomplexfilter'
poperty='name'
value='foo'
mode='contains'
GET /useres/filter/mycomplexfilter
Hope this helps to shed some light on the topic
[EDIT]
See this summary for an explanation of the commonly used HTTP methods (aka verbs): Which HTTP methods match up to which CRUD methods?
See this question for a similiar answer.
Initiating a server sent notification (perhaps via SMS) should be requested using POST (e.g. to the ressource URI /notifications) with text and recipient in the payload. HTTP headers could be used to indicate the desired type of the notfication, while the HTTP status codes indicate the success of the sending attempt. Status code 201 indicates successfull sending of the message, returning also the URI for the newly created ressource.
Client request:
POST /notifications
recipient="+0049123456789"
text="this is the SMS text"
Server response:
201 - Created
Location: /notifications/9876