2-3 month old babies

It's been a while since my babies were that young but I'll do my best....some babies are actually sleeping through the night by then; closer to 3 months I believe they will smile back at you and definitely recognize by face their parents; hold their heads more steadily; I also remember my kids doing what appeared to be crunches by lifting their head up almost like a sit-up/crunch but I'm not sure if it was as early as 3 months or older.