relative pronouns - Comma before a participial phrase

I have two cases.

a) He sent me a letter written in English.

b) I was given a cup made in China from my friend.

I personally think sentence (a) should be non-restrictive since there is only one letter in question and the writer is not trying to specify which. So if you were to write this sentence using a relative pronoun, it would look like this: "He sent me a letter, which was written in English." My question is whether to leave the comma when you leave out the relative pronoun and be-verb. I did read articles saying unless the participial phrase is modifying the subject, don't put a comma, but I'm not sure if it applies to the non-restrictive participial phrase also.

As for sentence (b), is it okay to put "made in China" at the end of a sentence, i.e. I was given a cup from my friend made in China? Here, I think there should be a comma in front of "made in China" because that phrase is not modifying the word immediately preceding it. So which is "passable" of the following?

1. I was given a cup from my friend, made in China.


2. I was given a cup from my friend made in China.

Thanks guys.