Vulcan 22 series Gas Wall Furnace Chimney

Likely too old for an Energy Star Rating.

https://www.google.com/search?q=Vulcan+gas+wall+furnace+series+22+energy+rating

What is the efficiency of a gas wall furnace?
Wall Furnace Energy Efficiency Ratings

Today's wall furnaces are often rated at 80 to 90 percent annual fuel utilization efficiency (AFUE).Jan 26, 2021

Everything You Need to Know About a Wall Furnace - Family Handyman

Any furnace providing heat where it should and has little to no heat from its exhaust is doing a GREAT job ;-)

Our high efficiency gas furnace was installed with a PVC pipe as a 'chimney' which bothered me to no end until I found the surface temp of that plastic pipe only barely warm to the touch- that is a home run!

Usually these numbers on most other untits are stamped on a metal plate which is located
or attached to the gas valve, which would also give the BTU Input/Output. Probably the
Model Number as well

If I understand correctly, your Bock gas water heater vent is causing water to leak down into chimney.
This is a very serious concern

Water leaking from water heater flue indicates improper venting.
The hot air gasses from water heater combustion contain water vapor, but the gas should vent out of house before condensate forms on pipes.
http://waterheatertimer.org/Water-at-bottom-of-water-heater.html#flue

The problem might be caused by a power vented furnace that pushes vent air from furnace down into flue pipe for water heater. As a result, the water heater doesn't vent properly.
There could also be a clog.
Light a match under water heater draft hood and see if smoke from match travels instantly upward.

There are two major concerns.
1) If vent is not working, it means that odorless CO gas is entering home instead of venting outdoors.
CO carbon monoxide is deadly poison.
http://en.wikipedia.org/wiki/CO_poisoning
This is a very serious concern
You can buy CO detector after vent is repaired.

2) Water condensate will eventually rust away vent pipes because of acidic content of the combustion vapor. It can be expensive to replace pipes, and pipes with holes pose risk of CO poisoning.

My suggestion is call a qualified plumber ASAP and explain what you observe.
Plumber will want to inspect the vent pipes, and may want to extend water heater vent pipe up further inside chimney so furnace is not pushing air back into water heater vent.
Plumber may also find blockage somewhere in the vent stack or chimney.
Also post on a professional water heater forum like the Tank to double check anything the plumber says to you. These are the pros.
http://www.thetankatwaterheaterrescue.com/forums/forum3/

make sure you have 3 feet of vent pipe out of the roof and you have a UL listed vent cap, if you can re-light the unit all parts are good.

If it is a single wall vent pipe and it goes into a masonary chimney that
has double wall pipe, you can expect the temperature to be over 120deg.

If it is double wall vent pipe all the way to the roof, I would say that
the pipe might be under 100 deg. I guess I would have to no what type
of vent config you have.

If you think that it is way hotter than you can recall in the past, if it has a induced draft blower, make sure it is operating. You could take the vent connection apart at the furnace and make sure it is not plugged.

If you have a water heater tied in with the furnace vent. You could take
a lighter or a match and put the flame near the water heater vent, if it
blows out than you have a problem with your vent system.

Things that could cause this is another fan operating, a gas or wood
burning stove or an attic fan. Could also be due to the chimney vent
not being above the roof line and on a windy day could cause
backdraft.

my pyrox wall furnace has a digital pad it turns off & on but i cant turn the heat or fan uo or down its 4 weeks old

You may be smelling other products of combustion but CO2 is a color-less/smell-less gas. A water heater should be vented thru 4" vent pipe to either a chimney or a wye which joins it with another appliance and a larger(size must be calculated) connector which connects to the chimney. There can be no reductions in size as you travel toward the chimney, and all pipe must slope at least 1/4"/foot up toward the chimney. Single wall vent pipe can be used unless it is less than 6" from anything flammable in which case type "B" vent may be used with a clearance of down to 1". If all this is correct your chimney may be over-sized or obstructed. Proper venting can be very complicated and technical and takes up most of most installation manuals for any fossil fuel appliance.

Pleas rate my answer!

actually if you vent your furnace by code, it would probably be cheaper to have a chimney liner installed up the old masonry chimney. you may be able to buy a kit and do this yourself. any time a new furnace with a draft inducer on it is installed, it must be vented into the proper flu material. if it was vented into your chimney, it may not have be installed by code for your area. you may talk to the instaled if they are still available and maybe that can return and do it correctly. if you leave this vented into your masonry chimney, the acid content of the exhaust will ruin the chimney. a liner will also get rid of the water problem you have.

code 31 indicates pressure switch did not close or reopened during the heat cycle....1st thing to check is the inducer motor,,this is a small motor that turns a small blower wheel that draws the exhaust gases through the furnace and blows them into the vent pipe....1st locate the inducer assembly,,most easily identified by the small plastic fan blade that cools the inducer motor as it runs..1st turn off tstat and turn off furnace power switch..then turn on furnace switch,then set tstat to heat,set the temp above room temp by 5 degrees...remove the furnace front cover,locate the inducer motor,,if it isnt turning,but is warm or hot after a minute or so,likely the inducer motor is bad..if it isnt turning and isnt warm after 1 minute,then likely the main control board is bad,,not turning the inducer motor when it should,,,,,if the inducer motor is running,,then the pressure switch isnt closing,, could be a bad pressure switch but more likely there is a problem with the venting...some possible problems that would cause the pressure switch not to close in an 80% eff furnace [metal vent pipe] are: [1] a blockage in the vent pipe,base of chimney,dead bird at the furnace where vent connects to furnace or down inside the inducer assy,accessed by removing vent pipe from furnace....if all clear the chimney could be blocked up inside,,is the draft good when vent is removed from base of chimney?..if furnace is a 90%+ type [pvc plastic vent pipe],,then check the intake pipe at the furnace by removing it where it attaches to top of furnace..is the intake clogged with anything?..then check the intake and exhaust pipes outside for blockages,,including ice/frost/snow at the exhaust pipe outlet..