Re: Swarm life cycle questions?
It looks like a primary swarm & should contain a laying queen. The bees will live much longer than 6 weeks that's a common misconception.
It is not good to feed a brand new swarm. They are trying to get established and feeding messes them up.
Don't know why the bees have died / left, but the hive has been messed with quite a lot. Not your fault you are just starting out & have done the best you can.
But a new swarm should be installed and then left completely alone for several weeks. That's assuming the hive is set up properly, I know you had to intervene over the sagging foundation.
My guess, is that something has happened to the queen and the bees are drifting away. But leave it alone now. If there is no queen nothing you can do. If there is a queen it will pull through best if you leave it. You can have a quick peek in a week or so. In two weeks have another peek, if there are still bees but no brood, give it a comb of eggs & young larvae from your other hive.
44 years, been commercial, outfits up to 4000 hives, now 120 hives and 200 nucs as a hobby, selling bees. T (mostly).