Dryer vent duct

the rules are in the mechanical code. the spacing will depend on the material. since it is a dryer duct it has to be seamed the proper foil tape so there are not screws in the duct to catch lint. hanger iron held together with a bolt is certainly one option for support.

The more I look at it the less I like what you have. That is a major fire hazard. I just noticed that it is actually in contact with the breeching pipes from the water heater and boiler…

Without looking at your basement, I can't tell you how to reroute that disaster — but there has to be a way. Use rigid duct and hangars.

some guidelines from a building code. Your local code may vary, and manufacturers requirements apply

https://codes.iccsafe.org/content/IRC2021P2/chapter-15-exhaust-systems#:~:text=M1502.2%20Independent%20exhaust%20systems.,the%20moisture%20to%20the%20outdoors.

There's no reason the pipe can't go in front of the sanitary pipe.

The min thing on the ducting is that the pitch should be consistent, if it's there at all No dips. No humps. I don't know what your local code says — different locations have different codes..

sounds like your getting ready to sell.
if you are I wouldn’t worry about it.

I don't think you need much clearance. B vent only needs to have 1" clearance from wood.

unless there is some other circumstance like a point load is directly above it or it has been cut and patched a lot and they didn't weave the patches in, for an 8" wide opening you don't need a lintel.

if you are putting a breech in a chimney you would line it with a thimble that will seal the passage to the liner and support the chimney although as long as you aren't cutting near the corners it will be fine. the bond between the bricks will support it over a small opening like that. if you cut n opening every couple vertical feet it would be different but the bond of the bricks, the way they are interwoven, will transfer the force out to the corners.

i believe it is steel and is right here:

it gives me "network error" when i paste an image but if you zoom in you can see a metal thimble in the breech

sometimes unqualified individuals or people cutting corners will just knock a hole in the chimney, stick the smoke pipe in the hole, and mortar around it but there is supposed to be a steel or clay thimble there.

it is supposed to be within 6" of the bottom of the opening through the middle of the chimney, it shouldn't be say 3' above the foundation so you can't reach debris all the way at the base of the chimney. the frame and door doesn't need to be out of a catalog, it can be fabricated by a sheet metal shop or fabricated on site. i'm not sure you need to add it if it wasn't required when the chimney was built.

Get a level II inspection of the chimney first. Look at all the spalling near the top. A lot of freeze-thaw damage on that cold exterior chimney. Reline it with a properly sized smooth wall 316Ti or 316L ss liner. Sweep the liner into the Combustion Appliance Zone and cement in place. Once in the room, split it to the DHW and boiler, which btw appears to be running downhill. If you sweep it into the room, as allowed under the IRC Ch24, you don't need a clean out for gas.

According to Ch15 of the IRC, the max length of a Flexible Transition Duct or 'Slinky' is 8 ft. it can only attach to the appliance and not start further along. It must be stretched until the inner lining is smooth to maintain the minimum cross-sectional area. No male down fittings such as that band clamp on the elbow. Any Slinky must be listed to UL 2158A. It is not approved for direct contact with those hot vent connectors.

You need to rework those vent connectors, min. 3 screws per joint equidistantly spaced, no seams from 5-7 O'clock pitched up towards the chimney 1/4" per LF. The larger connector must be heavier gauge pipe. I'd replace that crummy ground key gas cock on the WH.

Ask Hector the Inspector how he wants it terminated: as-is or extended with hard duct out from the building 3 feet supported.

I would skip all the flimsy material and just run a continuous 4" smooth wall 316ss chimney liner as your one-piece exhaust duct. It exceeds the code. Use a ss wall termination extended out from the bldg. 3 ft. with a strong steel hanger off that post and angled away from the wood.