This will likely be a location specific issue, so it doesn't hurt to check your local codes.
All the fire rated work that I've done has been between units (both to other units and common areas) and any load bearing structures of a multi-unit dwelling. When we do that, fire blocking is installed in the ceiling space as well to prevent a fire from traveling through the ceiling to another unit. For everything else within a single unit, and in a single family home, we don't use any fire rated drywall.
Edit: A few reasons I'd disagree with Eric on this one. First, I'm presuming you already have a certificate of occupancy (or someone did) to move in with an unfinished utility room. That required an inspection that presumably allowed the space as is. Next, most codes for combustion devices (furnace, gas hot water) require that you have ventilation. Installing a vented door is perfectly acceptable and won't provide any fire stopping. And, finally, most HVAC's (if the furnace is forced air) will be connected to vents that run to every room in the house. From the little I saw, the furnaces and utility rooms in searches likely referred to multi-unit dwellings, and that does need to be fire stopped. You also have to use fire caulk around every hole. Our multi-unit buildings also have sprinklers throughout and spring loaded vents that snap closed in event of a fire.
That all being said, there's absolutely nothing bad about installing fire rated material around the furnace, other than the extra cost and that it's a bit more difficult to cut. If you want to do it, then by all means, do so.
Edit 2: One last note, realize that fire rated drywall increases the resistance from 30 minutes that you'd typically see with 1/2" drywall to 1 hour. Fire rated doesn't mean fire proof.
Sounds like plaster walls and the ceiling is gypsum boards covered with just a skim coat of plaster. My house in the midwest US has a similar setup. It was during a transition period (40s-50s) from lathes to gypsum boards so the walls have lathe and then rough and finish plaster but the ceilings have gypsum boards covered with a thin finish plaster.
To hang pictures and stuff, I typically start the hole with a drill to get through the harder plaster layer and then tap the nail in the rest of the way. For heavy shelves in the closets, I've drilled holes and used those plastic inserts you tap in with a hammer and then put a screw into.
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Went through this recently myself.
I'd try to limit the joist-to-joist out-of-flatness to 1/8" or less. If it's an obvious part of the ceiling, try for 1/16".
Get a long straightedge and a pile of drywall shims. High joists are pretty easy: add shims to bring them down to flat with the others. Low joists require you to build up the adjacent joists gradually over a few joists to meet that 1/8" (or 1/16").
I attach the shims with staples, but many people like to glue ceiling wallboard in place, to prevent dimples at the screws/nails in the future. If this includes you, then the shims should also be securely glued.
Once you get the drywall up you can somewhat correct ridges and valleys with a repeated skim coats of joint compound. However, it's difficult, messy, and much easier to fix the framing first.
36" Drywall Shims: (menards.com)