You can say
What do you mean?
to ask someone to clarify something they said. Or
What is the meaning of this?
to express outrage at someone's actions or a situation. Or
What is the mean of the data?
to ask about statistics.
Edit
For the ring-in-the-ice-cream scenario, you might ask,
What does this mean?
But really, a ring in your ice cream is so surprising you might simply ask,
What is this?
The difficulties with your examples arise partly from the use of the verb come as well as with the tenses.
It's clear that you are speaking in Example 1 after you had gone to the party. You are no longer at the party. Therefore you need to say that your friend went to the party. If you were still at the party, your friend would have come to the party.
That's to say, you use come to mean towards me and go to mean away from me or in some other direction.
This is slightly complicated in your examples because you are imagining yourself at the party when you write them.
To avoid this difficulty, you might write:
If I had not gone to the party, I would not have met my friend who arrived there/showed up there/turned up there/was also present.
Example 2 is more complicated. You are writing it before you decide whether to go to the party:
If I did not go to the party.....
You conclude that:
I would not meet my friend
which is perfectly correct
But because you are not at the party, which you may or may not attend, you need to conclude:
I would not meet my friend who is going there/going to be there/will be there/will also be there, etc
But you cannot say: who came there because you are not there yourself and because this uses the past tense to describe an event that lies in the future for you.
Best Answer
Building off @TRomano's comment: Both the short form or the long form can be used depending on context. If you are writing software and generating an error message or throwing an exception, the shorter form is acceptable. The 'to be' verb is usually dropped to keep the messages shorter.
In a more formal situation, such as if you were explaining in an email to a customer that the feature is not implemented, you would use the long form.