In this case the phrase "an only child" is correct because there are, in fact, many "only" children. "Only child" is a term that just means a person who does not have brothers or sisters. Many millions of people have no siblings, so each of these people is an only child.
In the context of talking about a specific family (or group) with only one child, you use "the".
Rachel, the only child present, toasted with orange juice rather than champagne.
On the other hand, when discussing (as a generality) people without siblings, you would use "an".
I was surprised to learn that Billy had no siblings. His care for younger children was not what I had been led to expect from an only child.
Either option would be correct and sound just fine.
I have a right to vote because I’m 18.
I have the right to vote because I’m 18.
Sometimes the definite article is assuredly the correct one to use, and sometimes the indefinite article is the correct one to use, but other times the difference is so insignificant that it doesn’t really matter which one you use.
Additional context might tilt the circumstances one way or the other, but, in this case, either one of those is acceptable and they pretty much mean the same thing.
Put another way, if someone is standing in line at the polls, and they say:
I have a right to vote in this election!
or:
I have the right to vote in this election!
no one is going to correct their grammar because they used the wrong article – no matter which version was uttered by the prospective voter.
This would hold true for other rights as well:
We all have a right to pursue happiness.
We all have the right to pursue happiness.
When we say the latter, we are referring to a specific right. When we say the former, we implicitly acknowledge that we are not talking about our only right. But no one will hear the latter and assume it implies we have no other rights.
You can even switch them around in the excerpts in your question with no adverse effects:
The right to life, the right to choose; the right to vote, to work, to strike; the right to one phone call...
Some examples of human rights include:
A right to life.
A right to liberty and freedom.
A right to the pursuit of happiness.
Best Answer
In case of emergency, use "in case of emergency" because it shortens the time to read it. Like said in the comment, it's an idiom, that does not necessary follow the grammar rules.
Sometimes, it helps, if you check such phrases in official documents. The good enough way to do this, is to limit the search to .gov, so site:gov "in case of emergency" (in quotes). I've got 446,000 results.