1a. Blind Corner Cabinet Depth

If the sink cabinet and the cabinet to the left of the sink are both 26″ deep, then the blind depth on the blind corner cabinet must also be ordered at exactly 26″. The blind dimension should always match the depth of the adjacent cabinet, in this case the sink cabinet, as shown in your drawing.

1b. Adjustable Shelf Removal in Blind Corner Cabinet

Possibly. It depends on the size of the cabinet opening and the blind dimension. I cannot say for certain without physically building the cabinet and attempting to remove the shelf. If the opening is too small relative to the shelf size, the interior adjustable shelf may not be removable after installation.

1c. Built-In Fillers on Blind Corner Cabinet

Blind corner cabinets include built-in fillers. Specifically, the cabinet you are using appears to be this one:
https://www.barkercabinets.com/product-p/b1dblindcornerrightv2.htm

This cabinet includes built-in fillers that extend from the face of the cabinet to create a clean and seamless transition into the adjacent cabinet run. Please refer to the top-view images on the product page for clarification.

2a. Bi-Fold Glass Door Availability

We do not offer a bi-fold glass version of that cabinet. The bi-fold hinges would be visible behind the glass panel, which would negatively affect the appearance. To prevent aesthetic issues and unmet expectations, this configuration is not offered.

2b. Glass Door Hinge Visibility

Same as above. Unless the glass is highly opaque, the hinges will be visible behind the glass panel.

3. Glass Installation Information

For glass installation details, including how the back of the door is prepared and how glass is installed, please see this video guide:
https://www.barkercabinets.com/cut-and-install-cabinet-glass-s/355.htm

You may also choose to have a local glass company cut and install the glass for best results.

4. Dishwasher Appliance Case Requirement

In your situation, the dishwasher does not require an appliance case. Appliance cases are typically only needed when the dishwasher is located at the end of a cabinet run or in situations where additional countertop support is required.

5. Full-Height End Panels vs. Toe Kick Clearance

Based on experience, I strongly recommend holding the finished end panels up 4″ and allowing the toe kick to run underneath, rather than running the panel all the way to the floor.

There are several advantages to this approach:

Easier cleaning access

Reduced risk of toe stubbing

Less long-term damage from foot traffic and cleaning equipment

Improved durability and appearance over time

Full-height panels that sit directly on the floor tend to get damaged more easily and are less practical in everyday use.

6. Overall Review

Everything else looks good.

1. Correct, the adjustable shelf inside the blind corner cabinets is not required. You can simply not install it if you wish.
Sure, see the attached image for a top view of this cabinet at 46″ wide with the 26″ blind. https://www.barkercabinets.com/product-p/b1dblindcornerrightv2.htm

2. 12″ to 14″ will all work. I prefer 13″ for wall cabinet depths because it accommodates larger-diameter plates without them contacting the back of the doors. However, either of these side returns will work fine.

3. 3/16″ thick glass is what I used in the video, and it was easy to work with. It was sourced from the local Home Depot, so it should still be readily available. If you cut into the radiused notches in the back, you can use thicker glass, as some textured glass materials can be up to 1/4″ thick.

The upper corner configuration shown in your picture is not something we offer. The issue is that one door cannot open fully because it will hit the knob on the opposing door. This means you would have to open the knobbed door first, and then manually pull open the other door without a knob. If you look closely at your picture, the right-side door does not have a knob for this reason.

It may function a bit awkwardly, but I understand the appeal. Some of the wider 90-degree wall corner cabinets can have issues with bi-fold doors sagging over time, which is why we limit the sizes of those cabinets on our website.

Overall, if we offered the version shown in your picture, it would likely lead to customer complaints about the functionality of the design.

A 29 inch drawer is very common as far as width is concerned. I personally have 36 inch wide drawers in my island loaded with cast iron pans and have had no issues using 1/4 inch thick drawer bottoms.

What people need to understand is that you can always add reinforcement to the bottom if needed. After installation, you can inlay another 1/4 inch or thicker panel into the bottom of the drawer box if you want additional strength.

The reason drawers are not built with bottoms thicker than 1/4 inch is due to the dovetail construction. Anything over 1/4 inch requires a deeper dado, which will cut into the dovetail joint in a way that can show through as a visible gap or void once the drawer is assembled. If someone is offering a 1/2 inch drawer bottom, they are typically notching the bottom to fit a 1/4 inch dado, modifying the dovetail joint to something non standard, or adding an additional panel after the drawer has already been assembled.

A better option for heavy cast iron storage is to add a 1/4 inch to 1/2 inch rubber or vinyl liner to the bottom of the drawer. This is not so much for rigidity, since 1/4 inch bottoms are more than sufficient and I have never had one reported as damaged, but to protect the finish. Cast iron can scratch the bottom surface, and any residual moisture from a pan that was not fully dried can cause rust stains. Those stains are difficult to remove and the drawer bottom is not easy to replace.

I have kids, and they do not always dry everything perfectly after dinner. Adding durability where you can helps prevent unnecessary frustration later.