Talk to your town's planner or code enforcement officer and find out what the rules are. Get a copy of the neighbor's building permit (It's a public record), probably available on line, as is the building code. You may need to talk to an attorney. But between the rules and their permit, you may find the answers. You want to think clearly about your proposed remedy if they are violating the rules, don't settle for something the propose. (Among other things, make sure the pony wall is on their side of the lot line.) If the building code is incredibly long, don't be intimidated. In the city nearest me, it's nearly 1000 pages, but most of it is highly repetitive. They repeat the same definitions in every zone and you only have to read about your zone.

When attaching roof drains to underground drainage, I've used perforated PVC piping up to 40 feet long. Dumping all the water in one spot in clay can be a problem. So much easier in new construction--a few swipes with a backhoe! You can also go the dry creek route. Source: Backyard Boss

It is my belief that you must solve the drainage issue before anything else. Don’t understand the sump pump comment - is one outside? The photo appears as though the grade is away from your home/patio. Perhaps a French Drain directed to a lower discharge point will be necessary. Your Plat of Survey should indicate elevation(s) - have a qualified landscaper/nursury guide you.

>Does the proposal from the plumber make sense? No, not really. See below. >Because the water from the steam oven is so hot, I assume the extension has to be copper hose. Correct? The install specs I've seen for Miele CSO ovens always state "Only genuine original Miele hoses can be used with this appliance." And "Do not shorten or cut the supplied drainage hose." This clearly means do not use your own supplied copper tubing. A few things you wrote don’t make sense, probably because not all details are listed. The main thing is how you phrased what the plumber told you. Did the plumber a.) “suggest” this high loop after looking at your setup? Or b.) did he review the installation specifications and then “suggest” this? Based on what you posted my guess is he did not look at the installation specifications. I do not see that ‘high loop’ as satisfying the installation requirements and specifications. Here’s my suggestion: Get both of these documents (from the mieleusa.com website) for your exact oven model: a.) Operating and Installation Manual, b.) Specification Sheet. These are two different documents, and depending on the model and model year may use use slight variations on the document name. The first document is about 200 +/- pages and you want the section on drainage connections. The second document will be about 20 +/- pages and it will also have a section for drainage connections. Preferably find a different plumber than the one you talked to above. Tell the new plumber you have a problem with the drain connection on a high-end plumbed in steam oven, and you want to employ him to review the specifications for the oven and tell you if the plumbing on the install is done according to the manufacturer’s specifications. Because you suspect it is not. If new plumber grumbles or resists “we don’t need to read no specifications…” find another plumber. Good plumbers who do kitchen and bath remodels are used to researching things like this and will have no problem doing so. If the install already meets the specs and you still have a problem then it’s time to contact Miele service. Last point, suggest you question who ever designed your arrangement to find out if he/she followed the manufacturer's specs (it sounds like they did not), and if not why not? Isn't that what you paid him/her for? Why all this talk of and fuss about manufacturer’s specifications? Because no matter if you are talking basic drywall, regular old concrete, hardwood flooring, roofing and rain-gutter systems ... or multi-thousand dollar hi-tech ovens, having something installed correctly -- to exacting manufacturer specs -- is the key to long life, to full warranty coverage, and to minimize failures. Short translation: If you want your oven to work correctly make sure you follow the manufacturer’s installation specs.