There are up/down arrow buttons to reorder in the UI, drag & drop didn’t make it in. With a bunch of services & rules you might want to look into selector rules, which let you define the routing rules on the individual services instead of editing the balancer every time. (Also not configurable in the UI yet, probably 1.4)
I dunno when that was or what to tell you without specifics, but health checks are the only way containers are replaced or pulled out of balancers when they go bad. They run on (up to) 3 hosts other than the one the target container is on, so you need the full mesh of cross-host-communication working (every host in the environment should be able to reach every other one using their registered public IPs).