Absolutely NOT as the drainage in CI piping has to enter at a 11/14 ,22.5 , 45 deg, 60 Deg as allowing a pipe to go straight in will erode the CI wall
If the drain is adequate size, 3inch, then you could.
Without knowing the layout or type of drain pipe and location, it is impossible to give a good answer. Drill a hole in the floor and run the drain with PVC. Drains should fall 1/8 to 1/4 of an inch for every foot of distance. Horizontal distance. There may be a drain line that is closer to the first floor location that you can tap into. Washer drain does not need a vent, it gets it's venting around the washer hose.
Heck no as the sink is higher then the basement drain and water does NOT flow up hill BUT it does seek its own level BUT you can connect a sink drain to a basement drain if you properly trap and vent the line
Yes. Unless it is going to a laundry sink (like in a basement) That is how they did it back in the twentys,thirtys and fourtys in oklahoma. There are still alot like that today.
A drain plug washer is not necessary unless you have oil leaking from the drain plug.
Connection of the washer drain hose to the tub drain is very important. This will help prevent leaks for example.
I have had it like that at a house I lived at, it would drain directly into the basement floor drain, however it was a pain in the behind, because I often found myself tripping over it, or if the kiddos wanted to ride their bikes or 3 wheeler toddler things in the basement they would get hooked up on the hose also. And if it got to far away from the floor drain I had a water mess, so if at all possible go with the drain behind washer, out of sight ... out of mind.
my washer keep on by passing the spin cycle and will not drain out the water.
The drain from the washer to the main line is getting plugged and the floor drain is easier. Drain cleaner in the floor drain should take care of it.
Hire a plumber.
sounds like you are going to need to install a sump for the sink to drain into and then you put a sump pump at the bottom and connect it into the houses main line.
A basement standpipe is an open-ended and watertight pipe inserted in a floor drain to prevent a flooded basement.