What would be the proper way to connect a new pvc vent arm to the cast iron vent pipe? The pvc is 1 1/2" and the cast iron inlet is the same size as the flex tube that is attached to it now.
It's hard to see the drain pipe because your camera is focusing on the brass tee in the foreground but, I think usually, in older homes (like mine), the plumbing starts off as galvanized pipe and transitions to cast iron at the building drain (the 3 or 4" pipe that goes to the septic or sewer). Your house may have originally had galvanized pipe all the way to the sink like mine did.
I had a similar situation as you but at some time in the past (before I bought the house) the galvanized pipe corroded and was apparently leaking.
You can see at the end of the trap arm, there is a trap adaptor on my old galvanized pipe. You may have something like this on your pipe sticking out of the wall.
If you do have threads there, then just get a PVC adaptor from fpt (female pipe thread) to 1 1/2" PVC (Or from Male Pipe thread to 1 1/2" PVC...whatever you case may be). From there you may have to adapt it to what your Hepvo needs...probably 1 1/4" PCV. It looks like the Hepvo comes with a PVC slip fitting. I would draw a sketch of what you know you have once you get your Hepvo and then take it to your home supply place (a small one if you want advice...like ACE or a locally owned hardware) and say , "I need to go from this to that," and show them your sketch.
In my case, Some time before I bought the house, they abandoned the corroded galvanized and installed a PVC drain through the floor.
Unfortunately, the PVC was installed incorrectly and they set up an "S" trap which is against code. I ended up using a sawzall to cut the old galvanized out and replaced the "S" trap with a proper setup using an AAV (Air Admittance Valve) for the vent. As a side note...as you are finding out, when you start working on kitchen sinks, it often opens a can of worms. I ended up replacing several wall studs and the sub floor due to rot.
Also, someone mentioned that after I replace the shutoff valves, I should run PVC all the way up to the sink line. What type of fittings would I use to connect the pvc to the flexible metal tubes that are there now?
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There are many choices for water supply. Copper, CPVC (not PVC ...against code for drinking water), galvanized (not used much anymore, or PEX (most used these days). I originally had a combination of galvanized, copper and stainless steel flex supply line on my old sink. I redid it with PEX and then the SS supply line.
You can see the brass to PEX TEE in there for the dish washer. IMO, PEX is the easiest to work with but it requires some tools (just like all the other types of plumbing). I use the Expansion PEX which is super easy but the expansion tool is expensive. I have a Milwaukee cordless expander. You also need a PEX cutter which is cheap. Some people like the crimp PEX and the tool is cheaper but a little more awkward to use.
My house still has a lot of galvanized in the crawlspace. I am currently adding a bathroom and continuing the removal of galvanized in favor of PEX so I'll get my money's worth out of the expansion tool.
