Broody hens sometimes wean chicks as young as 4 weeks. I've had a broody wean hers at 3 weeks in the summer and those chicks were fine on their own. It does depend on the weather. Yours are old enough to be outside during the day.
I don't know your low temperatures, but if you have daytime highs of 90, your lows should not be a problem at all. Rain should not bother them, but giving them an area to get out of rain if they wish would be a good idea. They will probably be out looking for worms in the rain once they get used to it. They will probably be frightened of rain the first time they see it, but they should soon adjust. Hopefully you live where it does occasionally rain.
I'd be more concerned about the heat. As long as that box does not get too hot and they have some shade, they should be OK, but make sure they don't run out of water. At that age heat is more of a danger than cold.
Coyotes, foxes, and many other animals do most of their hunting during the night, but it is not that unusual for me to see them hunting during the day. Seeing a fox or coyote during the day does not mean they have rabies, that they are sick, or anything like that. It is always wise to be cautious around a wild animal, but seeing one during the day just means they are out during the day. Maybe they had a bad night hunting? Maybe they have hungry babies to feed? Maybe they were recently weaned and are looking for a territory to call their own?
Your chicks are at more risk from coyotes and foxes at night because they are more active at night, but my biggest problems have been with dogs and they are active during the day. A predator can strike at any time. I don't know if those chicks are too big for the neighbor's cat to be a risk or not. I probably would not trust it yet.
You will probably be OK in that cage, but no cage or place is 100% secure. There is always something that can happen. That looks like it is made of 2" x 4" welded wire, which is pretty good. Some things, like a raccoon, could reach a paw in through the wire to grab a chick. To make that more secure I'd consider putting some smaller meshed wire around the sides to stop that. It will also stop the chicks from sticking their heads out to peck at the grass, which puts them at risk to some predators. They will normally be scared of any unfamiliar animal for a little while, but they can pretty soon become complacent.
I'd consider anchoring that cage so something could not knock it over. A dog is less likely to crush that if it is anchored. I'm guessing that it is 2' high (that is the only thing that makes sense) so you have a 2' x 4' area on the ground. That is fairly stable but it can still be knocked over by a big dog. But anchoring it may mean you can't move it to new grass, which kind of defeats the purpose of having them in a cage.
That 2' x 4' area should be plenty big enough for 6 chicks for several more weeks, especially if you can move it around to fresh grass regularly. But I'd really think about building them a permanent coop soon. They should be able to spend the nights outside without heat now and they will grow really fast. They will surprise you with how fast they grow.
I don't know your full circumstances, but I'd think they are fairly secure in that in spite of everything I've said. Remember, just because something can happen does not mean it absolutely every time will. But in my opinion, the best way to increase their security is to build them a permanent predator-proof coop.
Good luck!!!
