In fact we have an infinite collection of symbols.
We can use one symbol with subscripts on it.
For the first question, I have never seen existential instantiation put that way.
I can only guess what the textbook means.
Let me give you an example.
There is a brown object.
There is a dog.
Therefore, there is a brown dog.
Clearly that is not a valid argument.
But without the rule for existential instantiation we could us the same constant twice and arrive at that conclusion as valid.