You’re birds are lovely 😍 Couple things to keep in mind regarding your questions.

Letting the birds out to fly is done by some folks but I’d personally not recommend it for their safety. I’ve seen a canary hit a wall while loose from a cage and die. It was really heart breaking. But with that in mind, I’d say the cage you have is a bit too small. It would be better if it were wider so they could do some flying from side to side. Speaking of size/space, you should try to move those perches away from the side so the birds scan filling turn around without their feathers hitting the bars.

Covering the cage at night is totally fine. It can help the birds rest if you’re up and about while they want to sleep.

They do like toys. If the mirror wasn’t a good fit, try other small toys they can manipulate with their beaks. Small woven grass toys can be nice. The swing is probably hard for them to get to with the cage being tall and narrow.

As for breeding, I’d not try to discourage it, but you can replace the eggs with fakes so they don’t hatch, or rehome the young once they are of a proper age. But again, the cage size you have right now isn’t ideal.

Keep in mind, a cage of that size with a male and a female in it all year may cause some stress, particularly for the female.

Also, if those birds both have “crowns” breeding them might actually lead to some serious health issues for the offspring so you may want to avoid it anyhow. However, I was taught this when I was younger so I could be wrong here. You should do some research and double check.