Does it say what egg group a Pokemon is in-game? Is there anybody who tells you?
Simple as that.
Source: After playing every gen (albeit some a long time ago) I know this does not happen
Hope this helps!
This question is hard to answer. Even though I highly doubt it and never have seen it, I cannot find any information that says that you cant. The only source that I can give is my experience of not finding any mentions. I will update this if I find any other info.
The answer is No which is a shame.
So this means you have to find out online or in a book!
Source: Talked to every character in ORAS, XY, Pearl!
Also played every gen.
There might be info somewhere but I just haven't found yet.