1. I believe I saw that you live in Bensalem. My neighbors recently caught a parakeet landing on our porches. I find it suspicious and coincidental that both, you and I, have seen keets loose in this community. Your female with egg is probably an indication that she was let go by someone who had too many keets and are letting them breed? Probably nothing more than a "dumb human trick". If you take to to WHS, they will only keep a lost and found for 48 hours before adopting out or gassing.
2. I take my keet to Dr. Esteban Baeza. We are lucky to have this small animal vet in our neighborhood. He will teach you that they eat everything. Feeding only seed kills them. They are supposed to live 15 to 20 years on a balanced diet. Mine was raised on Tropamix (I buy it from The Green Parrot in Tullytown). In the meantime, I keep making birdie salads (no avocadoes), presenting a variety of fruits, brown rice, etc.
3. Your bird should stay quarantined. My rescue parakeet was from the WHS. He has an advanced case of mites. I give him water containing medicine daily. I mix it every 5 days. Easy to do.
4. Parakeets are very intelligent and talk. Go see Disco on YouTube
5. Hope this information helps. Tweet! Tweet!