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Hire a plumber.
You hire a plumber to put in a one way sewer drain valve.
You have to cut out a section of the floor so there is room for the drain. Something like a foot wide and 16 inches long.
Well first you make a basement and then you put stairs in it where ever there is a space for example if you where trying to put stairs in your house to the basement you would have to have a huge amount of space and delete 6 squares of floor and but 2 stairs then in the basement you put the stairs where 6th squares are then you have basement stairs.
Yes... is the short answer. The toilet has a trap in itself. You would have to be able to break out the floor and put a P trap in the existing line
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.
YES !!!!!!!! Minimum 2" P Trap Yes, and it needs a wye not a tee, and it needs to be vented properly.
yes you can as long as the floor stays clean and as long as the basement remains clean
Vinyl
Install a ty fitting on the stack in the basement then run it to the sink. Put it low enough to account for a fall in the pipe, to allow proper drainage. Be sure to install a waste and vent pipe to code for both fixtures.
Yes you can use elbows if in fact that it is a vent. If it is a drain from above then certain fittings must be used depending on the piping configuration.
Cheapest packaging.