No need to stop or failover.

Only the instances that are running on the current node can be patched.

Could try using the "Subscription never expire" option and reinitialize.

If this does not work , keep the last option as updating the table status

with 2 which is active state, and...

I think this question's answer is

c. An error occurs because the first restore statement is incorrect.

Reason :

the syntax of RESTORE DATABASE and RESTORE LOG wrong, it should be

RESTORE...

no problem you can proceed in your way

You can specify the total time, for which your trace needs to run, which can very gaurantee that the stop and start will happen at exactly the same time, by...

Ensure that you have a few minutes gap between the stop of the current trace and the start of the new trace, so that all the data in the buffer...

Are you doing it manually ?

You can set up a stored procedure and schedule a job that runs every day with new filename.

Ananth G