You need to use the "get_survey_list" API to get a list of survey ids, you can then feed these into the other API methods.
Note that a survey link is actually an individual collector for that survey, and not directly associated with a survey - i.e. it is associated with a collector, which is then associated with a survey. You can have multiple links (or collection methods) for one survey that way. You can get a list of collectors for a given survey using get_collector_list. get_collector_list can also return the list of URL links for these collectors, if they exist.
There is currently no way to get a survey_id without going through this method - these survey ids are not meant to be visible to the end user, usually for API integrations a list of the user's surveys is presented to them (via the get_survey_list method) and then they select one. If you're interested, have a look at Mailchimp, Zendesk or Hootsuite's integrations.