To answer a couple of things (as an ex funeral arranger)...
Yes people do rob funeral homes. Some are holding jewellery of the deceased, and some people still like to pay cash. Now, if the funeral home had good practice, the jewellery would be securely locked up in a safe, and any cash would be banked and not held on site, but sadly there will be some that don't have good protocols.
Storage of bodies. One of the branches I worked in had a cold room. It had four storage bays (each had four trays, so 16 deceased in total) and we could hold a few more in coffins in the cold room, so max of about 20 (though could have been more if the room had been bigger). Another branch had fridges rather than a cold room. In that room we could hold 24 deceased in 6 fridges, plus there could be up to 3 deceased in coffins if they'd been embalmed and the funeral was imminent. The funeral home in this article was either storing inappropriately, or they had a huge mortuary/cold room to hold 34 deceased.
In respect of comings and goings at 3am, this would not necessarily be something awful. We would get calls at any time of the day or night and would have team members on call who would be up and out of bed and off to a family to collect the deceased and bring them back to the funeral home. I always felt sorry for the houses closest to our branch as the noise of the metal shutters (at the back of the property where the private ambulance went in) going up and down in the early hours would probably have been annoying in the quiet of the night.
In the case of the funeral home in this article, it could possibly have been a member of the public who saw something, or it could have been a "hire-in" who saw something they were shocked by. It's not uncommon for funeral homes to hire in staff (eg funeral bearers) as needed, rather than keep permanent staff on the payroll.