Very inexperienced newbie.. Needing basics

Hi everyone, think we've made a massive mistake by jumping in too quickly and not doing any research. We have absolutely no idea what we are doing, never had birds before. We only went to look and ended up coming home with them.. (Although we all love them)

We have 2 peach faced love birds, supposedly a male and female of 4 months, any way to tell if this is true? We bought them from Jollies pet store-was this a wise idea?

They have what id consider a large cage, they have a swing, a little mirror toy and a cuttlefish. We plan to buy some sort of rope toy, anything else we need?

How long before they 'settle in' and become used to us? I live with my husband and have 3 children (7,4,1) so have a busy house. The birds are in the corner of our living room so see us all day, there is always someone home. Everytime we go near the cage they get so scared and fly up to the very top corner and cling to the bars and flap about, we havent let them out yet as are to scared they wont come back, our living room is all open plan up the stairs and the ceiling goes to the roof of the house so couldnt reach them no matter how hard we tried. How often do they need to fly about? Or rather whats the minimum time they could be out? And how do we train them? With treats? How old before we let them out?
Also, what sort of things can they be trained to do?

Sorry for extremely long post, like i said, very inexperienced and shouldnt have bought so soon.
Any advice? Needing as much as possible!!

How would i add photos?

You can have your lovebirds DNA sexed by a vet or you can take a sample yourself and mail to a laboratory.

Since they seem to be afraid, you shouldn't try to let them out in the open where you can't get them. Is there another room in the house with a door you can shut? You could also maybe look into a flight cage for them if you don't have a safe room to let them out.

Training with treats as reward works well. Toys like paper to shred was a big hit with my lovebird, this perhaps can be a reward too. Do not use any sort of punishment to train, it will only make them lose trust in you. Singing or whistling to them will usually make them curious and happy - sometimes this works as a reward too. Right now since they are afraid, give them lots of room. When they show curiosity toward you, then move closer and attempt more direct interactions. It will take patience. Since they sound like they are a bonded pair, they may not be too interested in making human friends, so you must be persistent and patient. They respond best when you are loving and not "pushy", respecting boundaries.

They definitely need toys to entertain themselves. Safe heavy-duty bells, raffia and woven grasses, yucca slices, soft woods "bird kabobs" all go over well. Also perches with bark they can chew off - toy and also any natural shaped wood perches are great for their feet. I also strongly recommend sisal rope over cotton, and do not think nylon and plastic ropes are safe for parrots.

Lovebirds are very smart and can be trained to do tricks, to fly to you, and even though they tend not to be great talkers, some even pick up a few words.

You'll do just fine. Not to diminish anything but love birds are certainly no large macaw. No need to worry about "jumping in too soon". Give them love and attention and you'll do great!

Are they caged together? Bonded birds can be a bit harder to develop a bond with, but can still be trained.
The best thing you can do is just be near them, in a calm environment, without trying too hard to approach them. As they get used to your presence, the next step would be to place an open palm with treats at the entrance of the cage. Let the birds come to you when they feel ready.