Your drainage pipes might have become clogged causing the water and solids to back up into the toilet. This makes it very difficult to flush. To test if this is the problem, just take a bucket of water and try pouring it into the toilet. If the toilet flushes normally, then there is no clogging issue.
Another issue might be that there is not enough water in your tank possibly due to leakages in the tank causing water to leak and empty the tank.
Another issue could also be the flapper valve closing too soon.
In a shower pan, the slope is the pitch from the perimeter to the drain which helps most of the water to run into the drain. However, there is till some water left. Preslope is for that remaining water that seeps into the surface of the floor to be caught by the shower pan floor liner. It's a slope that goes under the pan liner so as to make sure that any water that gets through the surface will seep down the liner to weep holes surrounding the drain underneath the shower floor, where again, it will be directed to the drain's pipe. Without this pre slope, the water will sit at the bottom of the shower pan and becomes a major area for fungi and bacteria. So to answer the question, pre slope is necessary.
There are two reasons for toilets to have an S-shaped pipe that leads to the drain.
One of them is due to the fact that the S-shaped pipe creates a siphoning action which make the flushing process faster. But even then it doesn't make any sense to have an S-shaped pipe since a straight pipe can possibly do it even faster.
There was a time when people did experiment with straight pipes but they caused their own problems. One of them is the smell. In an S-shaped pipe, the water that gets trapped blocks the smell from getting into your room. But for a straight pipe, there is no water to block the smell from the sewage pit to get to the bathroom leaving you with no other option other than to abandon your home. But other than the smell, the S-shaped pipes clogged water preventing insects or other pests from coming in to your home from bathrooms.
Deposition of the human waste in the septic tank also creates gas like Methane which if inhaled by humans could cause dangerous side effects like dizziness and headache. It can also cause oxygen depletion in the room causing you to pass out in extreme cases even death. There are many ways to die. But death due to shitting in a methane-filled bathroom just doesn't seem like the right way to die.
The S shape can also prevent some of the heavier objects you accidently dropped to go straight to the septic tank.