Hi Sanjay,

1. If you want to test batch then you can run below code from developer console and check the functionality..After executing the below code you can simply go to setup and check the schedule jobs and apex jobs and check the status there..

UpdateKBArticleNoOnCase_sched objUpdateKBArticleNoOnCase_sched = new UpdateKBArticleNoOnCase_sched();
database.executeBatch(objUpdateKBArticleNoOnCase_sched, 30); 

2. If you want to schedule this for every 10 minus then you can use below code
 Your schedule class and pass that to system.schedule method
 
 this will be your schedule class
 public with sharing class yourScheduleClassname implements Schedulable
{
    /// This method schedules the respective batch class based on given cron expression
    /**
    * Name: execute
    *
    * Parameters: SchedulableContext SC
    * Schedules the batch
    */
    public void execute(SchedulableContext SC) 
    { 
        UpdateKBArticleNoOnCase_sched batch = new UpdateKBArticleNoOnCase_sched();
        database.executeBatch(batch,30);
    }
}

Run below code to schedule it for every 10 minus

System.schedule('Scheduled Job 2', '0 10 * * * ?', new yourScheduleClassname());


3. Test coverage will be normal, you can first insert all necessary data and satisfy all condition and then you can use below code 

            UpdateKBArticleNoOnCase_sched objBatchClass = new UpdateKBArticleNoOnCase_sched();
            Test.startTest();
            Database.executeBatch(objBatchClass, 200);
            Test.stopTest();
            
            yourScheduleClassname objyourScheduleClassnameScheduler = new yourScheduleClassname();
            String sch = '0 0 23 * * ?';
           
            system.schedule('Test Territory Check', sch, objyourScheduleClassnameScheduler);


Please let me know if you need anything else on this..
P.S. If my answer helps you to solve your problem please mark it as best answer. It will help other to find best answer.

Thanks,
Sandeep
Salesforce Certified Developer