Radiant heat disaster

Looks pretty normal.

Circulate water though the exterior red pipes (so your wood boiler needs its own pump) and run the pumps to heat. You wire your thermostats to the black pump relays, these also have 24V supply if your thermostat needs it.

The plate HX can also be used to heat your hot water, depending on which direction your flow your boiler water, it can be priority over floor heat. No controls, but shouldn't need any.

Once you get it plumbed up and running, check the temperature setting on the mixing valves since you don't know what they are set for.

The white pipes might have been for a dump zone for the wood boiler.

Honestly, just start over. Leave the pumps, heat exchanger, and mixing valves (and maybe the copper and manifolds if you don't care about looks or functionality) but throw everything else away and start fresh. Wood boilers are almost always piped wrong and this is no exception. The underground lines (assuming they are the same non barrier tubing in the picture) are filled with groundwater now and will give off more BTU to the earth than the building. Dig them up and bury a single set of good foamed lines such as Thermopex, Rhinoflex, Insulpex, or Logstor. Nothing else is worth burying. You're going to need to flush everything to get the atmospheric crud from the previous boiler out of the lines, and to do this properly you'll need an additional heat exchanger (unless you don't want domestic hot water, which is the function that this one was previously serving, then you could reuse it for the radiant) and pressurize the whole radiant system with the appropriate closed loop components and piping.

The old wood boiler had a pump (or two) on it which circulated 24/7 through that heat exchanger on one loop and the white tubing on a second loop. Those two tees to the left of the heat exchanger allowed either of the two right zones to draw hot water from one through the mixing valve(s) and return cooler water back into the other as some sort of primary/secondary loop but it's very poorly executed. I do these wood boiler systems quite often and if this were my job, I'd throw away every component besides possibly the pumps and heat exchanger.

What make/model wood boiler did you order?

I think this is a bit of an over-reaction. Just because the original build used plastic and sharkbites, it doesn't mean it wont work. All the bits are there. Not pretty but will work.

I do agree about the underground insulated pipe, wrong insulation can get saturated with water over time making it ineffective. If your wood heat is cheap, not a big issue, you can look at it as free snowmelt.

Meh, it's a lack of knowledge more than anything. I've seen hundreds of OWB systems installed by "professionals" that look worse than this. The biggest thing with OWB is that most owners are burning wood to save money, so they often end up hiring the cheapest plumber they can find or do it themselves with some guidance from their uncle Bob's dog's neighbor's brother in law and they end up with a clusterF like you have on your hands. The beauty of hydronics is that it's very versatile and even the crappiest of installs will still move heat from one place to another, but almost never are these OWB systems done correctly and yours is no exception. If you want it hacked together, it wouldn't be tough to make a few connections to what you have and make it work. If you want it done properly, starting over is your only option.

Not facetious at all. Just not sure if when you say "throw everything else away" you're including that. Because I agree that the OP is probably better off assuming that nothing on that wall is going to be of use. But it seems that if the in-floor coils aren't leaking or crimped they're pretty hard to screw up.

Lets objectively look at what is wrong with the setup.

1.The two loops share the same takeoffs so they are not hydraulically de-coupled.

2.Open system, no isolation.

3.Questionable underground piping.

1.This is a non-issue if the pumps have an IFC.

2.Most of the bits there don't care about oxygen. The pumps will rust. Sample of one, but I have cast pump on well water and going for over a decade, so they might be replacement item every 5 or 10 years. Wood boilers are maintaince, so that is not a huge item. The cost of doing this properly (HX,pumps, feed, regulator, expansion tanks) is many times more than the cost of budget pumps. You can also replace pumps with brass/stainless when they fail.

3. If your fuel is cheap, replacing that is not worth the cost of digging plus pipes. Doubt that juice is worth the squeeze.

That's for DHW

Usual outdoor wood boilers are unpressurized. This eliminates any pressurized boiler testing requirements. It also introduces air into the system. This issue is mitigated by use of highly inhibiting corrosion inhibitor. No idea how good it is but this is what they use. Even with non-ferrous materials, corrosion is possible without corrosion inhibitor.

We did similar open systems for solar thermal but used non-toxic propylene glycol auto antifreeze. It has better inhibitors for this type of system. Never had any issues.

First step as mentioned before is to pressure test with air or water to see if everything is intact.

Are you considering another outside wood boiler? Not a big fan of them but they have their place, I guess.

Most outdoor boiler companies sell some sort of inhibitor.

If you are considering an indoor boiler like a wall hung gas unit, then either corrosion inhibitor or automotive non toxic antifreeze would minimize eventual corrosion issues.