If there's enough head room then putting the toilet under the stairs could work. I like the layout you suggest with the tub/shower on the 6' wall and sink on the longer wall. Or you could possibly find a way to use the area under the stairs for storage. [Contemporary Powder Room[(https://www.houzz.com/photos/contemporary-powder-room-ideas-phbr1-bp~t_713~s_2103) by Seattle Architects & Designers Dan Nelson, Designs Northwest Architects [Transitional Powder Room[(https://www.houzz.com/photos/transitional-powder-room-ideas-phbr1-bp~t_713~s_2112)

Do not be too quick to dismiss your previous plumber for suggesting a AAV (Air Admittance Valve, "studor vent") for your kitchen island. Although the Uniform Plumbing code(UPC) & International Residential Code(IRC)have radically differing views on how a kitchen island vent is to be constructed, nonetheless, both the IRC & UPC do allow an AAV for kitchen island venting. Under the IRC all structures are required to have one "Main Vent",which must run undiminished in size from the structure "Main Drain" through the roof. After that we are permitted to install an unlimited number of AAV's. Under the UPC they do not require a "Main Vent" but all fixture vents are required to be sized by the total DFU (Drainage fixture unit) load of all fixtures served by that vent. Under the UPC a structure is only permitted a maximum of one AAV, with the expressed written consent of the local inspecting authority, and in most cases a kitchen island is the only location where they will grant the exception. Now what is the difference between the kitchen drain and your bathroom drain you ask? When we have a sink on an island it is generally the only fixture attached to that line. As the water drains from the sink it pushes the air ahead of the water in the pipe. Under some circumstances this can result in a slight vacuum in the pipe behind the moving water. This partial vacuum would then result in the standing water in the trap being sucked into the pipe by siphon action and once the water has passed on down the trap is left dry, allowing sewer gas to enter the structure. In this case we install an AAV, which would permit air to enter the pipe behind the liquid flow, thus negating the suction effect. There is a slim chance that you might resolve your problem by installing an AAV on the lavatory drain line, an when you consider the cost of installing an AAV as opposed to opening walls it might be well worth your time to try it, however I suspect you have a different problem in your bathroom. You state that you hear a gurgling sound in the tub or lavatory when another drain is used. It is possible that the water in the gurgling trap is being sucked out, and in that case an AAV might resolve the problem, but I suspect you problem is not a result of negative pressure (the partial vacuum) but rather it result from positive pressure. As the water from one fixture flows through the pipe it pushes the air ahead, causing a slight positive air pressure. Normally that positive pressure would be pushed up and out a roof vent however if your system does not have the required roof vent as one fixture is draining it will push that air up through one of the adjacent fixture drains and out through the trap. Keep in mind that the air in the line contains sewer gas so as that air & sewer gas mix is pushed out you get the odor. The odor may seem greater at some times than others. That does not mean the sewer gas is not leaking because not all the component of sewer gas are odorous. In fact, one of the main gases that comprise sewer gas is totally odorless.

I recommend that you pick up a copy of a good basic plumbing book, which will provide you with the general information that you are seeking. Once such book is the Black & Decker's book entitled "Home Plumbing", and it give all the charts and tables that you need to figure out what size drains to use, how large the vents need to be, where they need to be located, etc. The biggest challenge with a project like this is the venting. If you use the main stack as the vent, you can't tie your new vent into the stack until at least six inches above the flood rim elevation of the highest fixture that discharges to the stack (typically a sink o the second floor of a 2-story house).

Great input. Thanks. We do have a (fuzzy) copy of the plans, but I don't see anything in the basement indicating where plumbing lines may go. Perhaps we're not far enough along in the process to have those drawings yet. This is the biggest reason why I have so many questions - it seems standard procedure to choose a list of options and sign a contract before actually being served any details on the options. And, if we hadn't had such an odd experience with the capped PVC in our current basement, I probably wouldn't have any concerns at all with the promise of a rough-in. *I should also add that we are actually asking these questions of the sales staff, but obtaining answers has been time-consuming. We're less than the 10th sale, so I suspect they just haven't compiled the answers yet.