If you do not have manage rights, you will not be able to checkout or execute the successor tasks without completing the predecessor.
If you have manage rights:
While checking out the successor tasks, application throws a pop-up to checkout the predecessor and successor both. If user selects Yes, then a new pop up appears to check out either successor task or both the tasks (successor and predecessor).
You cannot execute the successor tasks if the predecessor task is pending.
You can execute the tasks in any sequence after both predecessor and successor tasks are downloaded for offline execution.