New drain in a basement

I’m hoping to move my washer and dryer from an upstairs hallway to the basement. The new location has good access to water pipes, but no drain. It is about 10 feet away from the cast iron waste pipe for the rest of the house. It's also about 8 feet from a 3" PVC line that goes from the kitchen into the concrete floor, and presumably on to the waste pipe.

Is it possible to tap into the cast iron pipe to install a new drain line?

If I tie into the 3" line from the kitchen, will I overload the line if I use the sink and washer at the same time?

Is there any advice or warning you can give me about moving the washer?

I appreciate any info you can give me.