Hello @yi zhang and welcome to Microsoft Q&A.
On Question 2, my understanding is that this selection method is for your convenience while editing. The same information is stored no matter which you choose. Since the same information is stored, there is no difference when it is read later. This results in appearing to always be "Enter Manually" when you open it later.
The "From Azure subscription" is just to make it easier for finding the details initially.
On Question 1, "test connection" is considered part of authoring. The detail to realize, is , activities initiated by the Data Factory service (such as scheduled triggers) move through a slightly different channel than activities initiated by you through the authoring tool (such as preview data, debug pipeline, trigger now, test connection).
One requires a 'listener'.
Much more concerning to me, is the last part. It sounds like you are saying, the scheduled trigger fails after your authoring session ends. Is this correct?