Yes, they're both up under the dash behind the glove box. Easy to see.  The vacuum cark has a vacuum hose connected to it. 

If I remember right if you lose vacuum to the vacuum tank it stops working, no heat.  So your problem might be under the hood.  I had a problem with the hose splitting, and got used to fixing it when I suddenly didn't have heat.

I have been seeing coolant - not too much - on the passenger side after some running. It is not too much but cannot put the new carpet in…

manual says take the glove box out and then blower which is more accessible then.

the two hoses which I took pics seem fine but very worn and drops are coming from the top. I suspect water **** or vacuum ****. I need to see them before making a call but there is surely rust there. Are these two easily available for a 77 280z?

I cannot find the part number for the vacuum co*k and water co*k for a 77 280z. Can someone help me?

Also what is the purpose of putting a water co*k after the vacuum co*k? both seem to be inline with water coming into the heater core?

I took a quick look at the parts diagrams and couldn't find the vacuum water cokk, so I can't help you with the part numbers.

I can answer the other question, however...  The water cokk is controlled by the temp slider lever allowing you to control the temperature of the heater core. The vacuum cokk shuts off ALL water to the core whenever the system is switched to A/C (regardless of the temp slider position). Once in this mode, the slider no longer controls the water through the core (since it's off completely), but instead controls the temperature switch that cycles the A/C compressor.

So, yes... They are in series, but they serve two related, but different functions.