1. While executing the testcases, if we mark the testcase as passed. By default the ticket is linked with the test session.
This scenario should not be there as if the testcase is marked as passed there should be no defect linked to that testcase.

No, it test case is passed, you don't have to enter a ticket.
I just tested and it works as expected.
I you can, please try and reproduce on Demo (demo.projeqtor.org) and if you reproduce, please let us know which test session, wich test case so that we can test.

2. Also while executing the test cases we again have to select the testcase status from drop down. Even if I had already marked it as passed.
In previous versions it was not the case. This confirmation consume lot time to execute a single testcase.

I don't undertand your remark.
First, checking "ok" will mark test case as passed without having to "select" status.
Also we did not change things recently on this part, so there is no reason for things to change.

I am working on ver 6.0.0

1) V6.0 is quite old, consider migrating to V6.5
2) V6.0.0 is not a stable release, at least migrate to V6.0.8