Is there any way to detect and get information on a push-subscription on subscriber's side?
You have 4 tables For transactional replication (push subscription) at the subscriber's side:


MSreplication_objects 



  contains one row for each object that is associated with replication
  in the Subscriber database



MSreplication_subscriptions



  contains one row of replication information for each Distribution
  Agent servicing the local Subscriber database



MSsubscription_agents



  is used by Distribution Agent and triggers of updateable subscriptions
  to track subscription properties



MSsnapshotdeliveryprogress



  is used to track files that have been successfully delivered to the
  Subscriber when a snapshot is being applied




you can use this columns to monitor the status for your replication at the subscriber's side

SELECT login_time,
       last_sync_status,
       last_sync_summary,
       last_sync_time,
       spid 
FROM dbo.MSsubscription_agents