SHAREPOINT 2013 - Search Administration

Make sure the "Search Host Controller Service" services in turning on in server. You can use this management shell command: net start spsearchhostcontroller

As about search topology issue:
http://blogs.msdn.com/b/bkr_sharepoint/archive/2014/06/09/sharepoint-2013-search-topology-activation-error-quot-unable-to-retrieve-topology-component-health-states-this-may-be-because-of-the-admin-component-is-not-up-and-running-quot.aspx 

Hope this helps.

It seems like a unhealthy search service application.

The first thing you chould check is all the services of search are working or not. Second should to validate all of the search components like crawl, query etc.

I would rather advice to re-create the search service application so that you do not keep strugglling to fix something which might have at more than one issue.

Please let us know how it went.

Hi,

I understand that you cannot get the search host node controller started on the server that runs the admin component.  You can use taskkill to stop it, just find it's PID in process explorer or equivalent and then kill the process, if sc command does not work.  Then you can make sure that the admin component node.ini is not blank

C:\Program Files\Microsoft Office Servers\15.0\Data\Office Server\Applications\Search\Nodes<Node_Number>\AdminComponent1\Configuration\Local

the node.ini is inside the local directory

open it with notepad and see if it is blank.  If it is blank, take a backup copy of it, then delete it from the local directory.  Save the backup somewhere else.  start the search host node controller.  If the search host node controller does not start, you could try restarting at this point.  The search service application should have created a new node.ini in that location and usually just restarting the search host node controller is all that is required if the search service application is not too fragmented\corrupted\etc.