Flush valve sticks open when fushed and handle falls off

Your handle has probably become disconnected from the gate that closes and opens the valve. If it is stuck in the open position you are indeed lucky. Flush the tank and replace the valve. There is usually a metal rod that is screwed into the gate. If the valve sticks and you pull ******* the handle it can pull the threaded portion out of the "gate". If this happens, you have to get access to the valve and remove it. This is a big mess on a full tank. You should first pump out the tank and get it as clean as you can. Then remove the valve and replace it. I did this once.

follow this steps and fix it.
Adjust or replace a flush handle:

1. Remove the cover from the toilet tank (the higher part at the back of the toilet). If the handle is loose, tighten the locknut with a wrench. If the nut won't budge, apply penetrating oil and let it set before removing.
2. Unhook the chain from the trip lever and slide the trip lever, with the handle attached, through the hole in the tank.
3. Soak the handle threads in vinegar for an hour or so to remove mineral deposits, then scrub clean with an old toothbrush.
4. Reinstall the assembly, tighten the locknut and adjust the lift chain (see below).

Adjust the lift chain:

1. If the handle must be held down while the toilet is flushing, the chain may be too long. Shorten it by hooking the upper end through a different trip lever, or use long-nose pliers to open and remove some chain links. Alternately, replace the chain with a new one.
2. Some flush assemblies have a lift wire instead of a chain. If the wire binds against its guide, flushing is impaired. Loosen the guide with a screwdriver, then adjust it so that the flush valve falls freely onto its seat.

Maybe the heat control is bad, This may be a vacuum operated shutoff under hood on the firewall. They sometimes corrode and stop working. Vacuum line may be bad too, or came off. .Did you flush heater core.? ( Heater pipes [1 1/2 inch pipes] goes to firewall, one goes through shutoff valve. Disconnect both. may have to cut one in middle - buy hose connector to repair it first! Use water hose to flush both ways)

Most people have trouble with the flapper falling too fast and they get one with a float on it or one that drains water on the counterweight to keep it up long enough. It sounds like yours stays open too long. Get a flapper that will fall fast without any gimmicks on it. the shorter the chain is to the flush handle the better too.

replace guts of toilet with a Fluidmaster valve and flapper. replace handle.(left handed threads on handle nut)

certainly indicates that the unit is not holding water (hence not starting on every flush). as you are seeing water in the shower - this is obviously where it is going. It may be that the internal flap (non return valve) is stuck open or damaged. If damaged you can put a new non return valve in your 40mm pipe run where the shower pipe enters the saniflo - about a tenner from most suppliers.

SLOAN FLUSH VALVES ARE SIMPLE. IT DEPENDES ON THE PROBLEM. IF THE VALVE KEPS RUNNING AFTER IT IS FLUSHED THE RUBBER DIAPHRAM IS DIRTY OR OLD AND THE RUBBER DIAPHRAM IS GETTING HARD. AND STICKING. THE VALVE WORKS ON A VACUME TO CLOSE THE DIAPHRAM TO STOP THE FLUSH PROCESS. WHEN YOU PULL ON THE FLUSH HANDLE YOU BREAK THE VACUME THAT FORM ON THE TOP OF THE DIAPHRAM WHICH ALLOWS THE WATER TO FLOW AS THE WATER FLOWS IT IS ALSO STARTING TO PULL A VACUME IN THE TOP OF THE DIAPHRAM TO CLOSE THE DIAPHRAM AND STOP THE FLUSH.
AS THE DIAPHRAM GET OLD AND WORN IT GETS HARD AND DOES NOT MOVE AS FREELY AND STICKS OPEN AND WON'T LET THE VACUME CLOSE THE DIAPHRAM AND THE URINAL WILL CONTINUE TO FLUSH. HOPE THIS ANSWERED YOU QUESTION

Open the tank and examine the linkages between the handle and the flapper. If the handle is sticking, it sounds like there may be either mineral buildup or a stuck chain.

I'd suggest using a good brand of synthetic oil (which was actually developed a really long time ago for the armed forces for use in polar reigions) Most flushes loosen too much material all at once, causing blockage of the oil pickup screen. You can get a bit more cleaning and lubrication protection by adding a bit of marvel oil to the synthetic. Change just the filter (and lost oil) about every 1500 miles, till the problem subsides.