Is it safe to let puppies sleep in a cage every night?

If you take your Hawk out first

Yes, very safe, actually better for them so they can't get into anything dangerous. Plus it helps potty training.

Some people use what is called a crate - it is NOT a cage as most puppies or dogs (once accustomed to it) see it as a pseudo "den.  One breeder I knew started her puppies at about 5 weeks in an open plastic bottom HALF of a large crate - with NO DOOR.  The puppies slept in a pile (on bedding) in it and began to get USED to sleeping in a crate (but they were not CAGED) they could roam out from the sleeping area to got potty on newspaper covered flooring - which they did.  By 6.5 weeks she moved each one into a side by side plastic travel crates - she would send them home in. They started off in open crates, but progressed to a closed crate for PART of the day time, most of the time the doors were off or left penned open.

NO ONE should plan to use one crate - for two puppies once they go home.  Each puppy MUST have it own crate and ideally NOBODY (ethical) will sell two puppies to the same home.

It is much EASIER to get puppy acclimated to its new home, get it house trained, prevent destructive chewing (and/or kept SAFE) if NOT allowed to roam while you are ASLEEP.  It is normal for the puppy and crate to be placed IN YOUR BEDROOM and for puppy to whine & let you "know" it needs to go out rather than soil its bed.  Commonly, puppies 8-12 weeks must go out once or twice a night, so you can PLAN to set your alarm. accordingly (if you are a heavy sleeper).

No, it is not if they are with the mother dog UNLESS the "cage" is very large.  The mother could suffocate them if she rolls on them.

How many pups are you talking about and how old are they? And how big is the cage and where is it kept?

Why not - in fact using a crate is rather safer than letting a puppy/puppies run around when you cannot supervise what's going on.   Using a crate keeps them safe and out of mischief.  Each puppy should have his own crate however and you willl need to get up at least once (hopefully) a night to take the puppy out to empty.

The two I have/had, bought in after the last of our home-breds, slept in their crates from day one with us, and still do/did.  And lined up to go in there with a treat.