Here I will provide some concrete evidence that they were indeed married

Marriage is contract like any legal commercial contract under British Law and I suspect under any civil law in your country. It needs three simple elements:

1. Offer

2. Acceptance 

3. Communication of Acceptance

1. Was an offer made in the case of Ashile Sun and Li Changge? Yes, a marriage proposal was made by Ashile Sun in front of Changge's memorial tablet. We can clearly see this in Episode  46, 27 minutes into the video. He wrote that letter of offer with red envelope. In that letter, he promised to protect Changge the rest of his life, give her freedom, stay with her the rest of his life, dote on her, love her and give her happiness. 

And when Changge read that letter, it meant that the proposal letter had already been properly converyed to her. She understood Ashile Sun's intention to marry her.

2. Was there an acceptance? Yes. Episode 46, 28 minutes into the video, Changge accepted the marriage in front of her mother's memorial when she offered the three cup of wine. Please listen carefully when she offered the third cup. It is an explicit acceptance of his marriage proposal. She said very clearly, he will be her husband.

3. Communication of Acceptance to Ashile Sun. This was done at the Tree Trunk Scene in Episode 49. Please listen and you will know what I mean. Changge did not reject, but said there is no need for them to have any formalities. What are the typical formalities? They have no more parents. So, a formal Chinese marriage ceremony like those we normally see, having them all decked in red, bowing before their parents and bowing to each other, are all unnecessary as both of their parents are dead. They just wanted to be with each other the rest of their lives.

There is a fourth element, Consideration. But because marriage is not a commercial contract, we could argue that Consideration is not necessary.  

So, for all practical purposes, they were indeed married. 

Do all their friends know that they were married? Of course! Please look at E48, at the 40 Min 45 seconds mark, note that in front of all their good friends, Situ Lang Lang said he came to say goodbye to Ashile Sun and he called him the 'husband of my disciple'. And no one looked surprised or anything.