Notch out 2 x 10 for bath drain?

First time homeowner here. We have an outdoor faucet that is below rear deck, about 8 feet from ground. Indoors there is a shutoff valve and old copper plumbing that is connected to Pex plumbing. The home was built around 1900 and was nearly gut renovated around 2010. I am trying to decide if it's safe for me to use the existing valves and if an expert can gauge condition based on the pics and what I can say about it. I dont even know if the copper and existing valves are that old because it seems odd to leave it in if the rest of the plumbing is being redone. The shutoff valve was in closed position when we moved in few months ago. Before trying to turn it on I got a sharkbite shutoff valve to have ready in case the old shutoff valve wouldn't close or leaked. I planned to put it in the short Pex section that connected to the copper. The indoor valve seems to work though stem is rusty. The exterior valve for hose connection does leak a bit when it is opened. Water trickles from the stem, the more it's opened the greater the leak. Despite the valves mostly working, and not leaking when off, I plan to put in the new sharkbite 1/2" ball shutoff valve. But, if I go ahead and do that it seems like I may as well remove the rest of the copper, if it's something fairly straightforward for a novice. Thanks for any advice

I'm working on installing a new kitchen dwv, running the vent up thru the top plate, then running the vent over 30' to the main stack. I was looking at the old setup, and there is a 1 1/2" iron vent on the opposite side of the window that goes directly up thru the roof. IF I can cut this pipe, can I use this for my vent instead of running pipe all thru the attic? IF I can get this pipe to budge, I may be able to replace the iron vent, but I have had ZERO luck trying to remove iron vent pipe (see my post on the main stack vent iron pipe). The old system was a prob, cause the vent was at the same level as the drain.