The story above sounds very much like what happened to me. I had a couple single birds when I was a kid. Then a friend of the family asked if we would take their bird since they could no longer keep it. Well, the new bird was female and she took a STRONG liking to my male. She actually squeezed through the bars of the cage to get to him. We ended up buying a breeding box and eventually had two breeding pairs. We had 13 birds at one time, I also gave away one, in three big cages.
Besides the birds we had a cat. He had to be taught to stop jumping on the cages or swat at the birds. Yes, he'd often try when we weren't looking either. Eventually we could allow the birds to fly free in the same room as the cat without an incident but it took a while.
Together they can be very noisy and dirty. Besides the feathers ours loved to flap empty seed shells all over the floor and fling droppings on the wall.
Our parakeets were a joy to watch and interact with. Each one had a different personality. They ranged from Sammy who was an elegant lilac bird to Filabuster the nonstop talker and general pain in the rear for his cagemates. One lived to be 16 years old.
Here are a few suggestions:
- Get a basic parakeet care book. Read up on what a healthy bird looks and behaves like, illnesses and treatments, general care and what to expect from your pet.
- Buy high quality seed for general feedings and supplement with seed trees, treat sticks and cakes and special seed mixes (color tone, honey treat, moulting food, etc.). I'd often mix some of the special seeds in with the regular food otherwise they would only eat and fight over the treats.
- Set up a cuttlebone and/or a calcium block in the cage. Your bird will need this for their bones and feathers.
- Parakeets also need some gravel, either from the cage floor covering, perch cover or loose in a treat cup. This is for digestion.
- Buy some chew toys or sticks plus toys like swings, ladders and mirrors. Birds love to and need to chew. The other toys are for general amusement and exercise.
- Get a bird bath. These hook to the outside of the cage. I'd prop a door open with a twist tie and then attach the bath. Fill with about a 1/2 inch of lukewarm water. They love this especially on a hot day.
- Buy a few general medicines plus vitamins and have them on hand. The vitamins you can add to the drinking water. The meds are good to have just in case you need to treat an illness. The quicker the better for treatment and we had a few situations over a weekend and having stuff on hand was terrific.
- Keep them out of drafts and cool temperatures! Parakeets aren't as hardy as outdoor birds and can quickly get sick if exposed to these conditions. Remember, these are tropical birds. I'd put my birds "outside" in our enclosed porch, with the windows open a bit, only when the temperature was about 78 or above. Don't put them directly outside or in a window. Sometimes they can get "spooked" that way too.
- I never clipped any wings. I know many people do it as a taming tool. I preferred to leave them as is so they could actually fly for exercise (in a small, enclosed room of the house). Plus, it was for their protection if they ever did get loose while the cat was being trained not to touch them. Just make sure no windows, shades or drapes are open or mirrors exposed if your bird gets loose. They will fly towards it to get out and will either find an opening or smack their head or neck trying.
Have fun with your new pet.
So, if they all hatch I will own 17 parakeets (one of the first batch of babies was sickly and died 
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