Kitchen Faucet on utility sink

The faucet for my washer has been leaking a little, seems to be around the stem. There are two nuts under the handle, should I tighten one (or both) to stop the leak. Thanks

I have a small rental house that has a plugged up kitchen sink drain. The kitchen sink drain pipe in the basement is also leaking. I have no way of repairing the leak ( can't get a wrench in there) much less getting a snake through all the 90 degree bends. It looks like the plumbing in this house was installed incorrectly 80 years ago. The drain pipe goes down through the floor with no vent pipe. It takes a 90 degree turn through the wall to the outside, where it takes another 90 degree turn down into the front walkway. About a foot of it is exposed. I have no idea where it goes after that. It is a steel pipe, not cast iron. The main drain line is on the far opposite end of the basement and it does not join it, at least not inside the basement. Maybe it does under ground. Here is my plan: To install a new kitchen drain pipe on the inside of the basement along the wall all the way to the utility sink line and join it with a Y coupler. The pipe would go about 40 feet along one wall and about 25 feet along another wall and then 8 more feet along the back wall. How much drop per foot do I need for this pipe and is this an acceptable way to do it? Should I use 2" pipe?