Cute game with a fun premise!
I will say some of the colors and traits seem a little off - I had an egg that was purple and pink, and the parents were Mococo and Bae, there was a mutation, so maybe that's what caused it? Same with tentacles on a combo that didn't involve Ina. Thinking about it now, that makes sense, but if mutations could have effects like that, I think it would be good to explain that possibility to the player. Also I feel like sometimes the stethoscope just straight you gives you the answer, so maybe it should be worth more than 2 guesses, maybe only usable after a certain amount of guesses, or even do something like, grabbing a catch phrase from another member to throw into the mix, so it's not always just a dead giveaway, it would require you to think about the other information you know to filter one of the results out or something
Otherwise I like the banter when it happened (I think it occurred at guess intervals? I wasn't paying a lot of attention, but I think I had dialogue pop up at 5 guesses multiple times), the conversations really felt like they'd happen between the members, very natural.
I normally encourage submitters to return to their games after the judging period, but to be frank I'm not too sure how to expand on this idea meaningfully - maybe some special events when you save a certain amount of eggs, or vice versa, but nothing really solid. Hopefully you can come up with some fun ideas and implement them at some point. Thanks for submitting!