The toilet flange is usually above the floor level. You would have to cut it off the drain pipe and cap it. How you do this depends on what type of pipe the drain is made of. Even if the drain should be below the floor level, you have to seal the drain or sewer gas will come up from the drain.
The laundry waste pipe is fitted to the main drain near the toilet and the main pipe down the line past toilet is partly plugged, forcing the laundry waste up the toilet waste tube. You need to auger the pipe from toilet to outside. If all the piping is in ground you will have to remove toilet from floor to do this properly.
You don't have to have one, it just makes it a little easier. As long as the drain is flush with the floor, you can drill into the concrete and us anchors to hold the toilet down. The down side is that they tend to corrode over time and become stuck in the concrete. If you ever have to remove the toilet, they can break and that makes putting the toilet back harder. You can just bolt a mounting ring to the floor and use regular toilet bolts to hold the toilet. These can be easily replaced if needed.
the purpose of the toilet is to go #2 & #3 and for the waste that comes out to go down the drain and get clean and it does it over and over again
You would have to build a platform for the tub to sit on. About 3 inches if you are using a floor drain. There is a trap right after the floor drain so you would not need one at the tub. If possible you could position the tub directly over the floor drain but that would eliminate the floor drain which would be a problem if the basement every flooded.
Remove the laminate floor first
If you have a drain available. You may need to chip some concrete around the drain to install the bottom half of the drain. With that in place, set the shower over it and the top piece screws into the drain to form a seal. You can build a 2x4 frame and raise the shower up enough to run a drain to a sump or a floor drain.
Drain the excess oil out. Remove the drain plug.
They may be screws into the floor or bolts into the floor flange. They can rust or the flange can rust and no longer hold the bolt so that you can take the nut off. Use a hacksaw blade to cut the bolt between the nut and the base of the toilet. A new pair of bolts costs about $3. Tighten them down and cut off the extra above the nut.
The pedestal you should be able to slide it underneath it and then put glue down. The toilet, you can make a paper pattern and then transfer that to the linoleum. Split it in the back to go around the toilet. It is easy enough to pull the toilet, all you will need to do is replace the wax ring underneath it. Pick the toilet straight up and set it in the tub or shower so that water doesn't get all over the floor. Tip the toilet forward and back to get the water out of the drain in the base.
I would say that if water had never backed up in your floor drain, then backed up even after you had the drain line snaked, Roto-Rooter didn't do their job. Once a drain line is cleaned, it should drain like it did before the stoppage. As for plugging the floor drain, it is there for a reason, I would not plug it. There are several items manufactured that will allow a floor drain to drain but if the line starts stopping up they will seal the drain off to prevent water from coming out of the drain.
Washing machine drains into a floor drain? The drain need cleaning. Liquid drain cleaner may do it, or it may need to be snaked. Simple fix is to get a 30 gallon trash can, cut a small hole in the bottom, the size of a quarter and set it over the drain. Let the washer drain into that. The small hole will let the water drain at a rate that the floor drain can handle it.
I assume you have a floor flange in place or are replacing an existing toilet. The floor flange is what the toilet bolts to that holds it down to the floor. Some older houses use lag screws to hold the toilet down to the wood floor and in basements, lag screws and anchors are sometimes used directly to the concrete. If you have a floor flange, it should be at the level of the floor or up to 3/8's of an inch above it. This will allow you to use a standard wax ring to seal the toilet to the drain pipe. If the flange is below the level of the floor, use an extra thick wax ring or double up two regular ones. You want the wax ring with the black funnel shape piece of plastic imbedded in it. There is a slot on each side of the flange that will accept a bolt. Either 1/4 or 5/16 thick. Put the bolts in the slots on either side inline with the center of the drain. I usually put the wax ring on the floor and sit the toilet base over it. Lining the holes in the base with the bolts. Sit the base on the drain, straight down. With it in place, you should have to compress the wax ring some so that the toilet will sit on the floor. Grab the toilet on each side at the back where the seat attaches and lean on it with your weight. This will compress the wax ring and make the seal between the toilet and the drain. Push straight down without twisting the toilet. Install the washers and nuts on the bolts and tighten them carefully a little on each side until they are tight. Do not over tighten them because you can break the base. There should be a cap to cover the bolt with the toilet. Put the flat white washer on the bolt first, the metal washer and then the nut. The white washer has to go on the right way up so that the cup will snap over it. The edge is beveled and the slope on it should be downward like an upside down V. Now install the tank. There is a large black foam cone that goes over the center hole in the tank and seals it to the base. Set the tank in place and install the two bolts that hold it to the base. Use a rubber washer under the head of the bolt to seal the bolt to the tank. Bolts go in from the top. As with the floor bolts, tighten them a little on each side until the tank is tight. On most toilet bases, there is a small ridge in front of the hole in the back that the tank will rest on when it is tightened down enough. With the tank in place, install the supply line and the seat and you should be in business.