Learn German: Das Porzellan hat ja einen großen Kratzer! - The porcelain has a big scratch, you see!

Here, ja is a modal particle, not the word for "yes." It shows that the speaker is pointing out something obvious that the listener can also see, or expressing mild surprise. It translates roughly to "you see" or "look," adding emotion to the statement rather than changing the literal facts.

Could I put ja at the beginning of the sentence instead?

If you put ja at the very beginning (as in Ja, das Porzellan hat...), it goes back to meaning "Yes," like you are answering a question. To work as a conversational particle expressing surprise or shared knowledge, it needs to stay in the middle of the sentence, usually right after the conjugated verb.

Why does groß have the ending -en in einen großen Kratzer?

The word Kratzer (scratch) is a masculine noun. Since it is the direct object being "had" by the verb hat, it takes the accusative case. After the indefinite masculine article einen, adjectives in the accusative case always take the -en ending.

Does das Porzellan just mean the material, or can it mean the actual dishes?

It can mean both! While das Porzellan literally refers to the material, Germans frequently use it exactly like the English word "china" to refer to plates, cups, and bowls made out of it.