First question: The i.e., which means "that is", is unnecessary in both sentences. It's clear from context that "an animal with thick skin and nails resembling hooves" is a definition of "pachyderm". However, it isn't necessarily incorrect, just verbose.
Second question: Yes, the comma is necessary, but style manuals don't all agree on whether the second comma is required. Some publishers don't require it, some do, and some forbid it.
Third question: "When should I use i.e.? Answer: When it isn't clear that what follows is in apposition. Two good examples of when i.e. is useful:
"He did not respond, i.e., he declined".
"Eating squirrel taco without any ranch dressing is like playing leapfrog with a unicorn, i.e., a very bad idea."
In both sentences immediately above, it's not as clear as in your two sentences that the final phrase is apposite to the initial clause, especially in the second example: What exactly does "a bad idea" refer to?
Rule of thumb: Avoid these Latin abbreviations whenever possible if they seem superfluous. Always avoid unnecessary words.