Maximum hole size in brickwork before a lintel is required

As general, design of lintel is much similar to designing a simply supported beam, depending on the architectural purposes, you can easily get the loading and do the design without involving complex analysis.

1. The height of the opening (hole) is irrelevant to the design on lintel, however, greater height of the opening would also directly indicates that the stiffness of the wall is reduced and may required stiffeners to strengthen the wall at its week axis.

2. For construction wise, rectangular opening is easier to construct. Circular hole would sometimes requires hacking and cutting of brickwork, and its best to avoid such activities.

3. Yes, totally, double leaf solid wall would logically be the heaviest amongst, unless the cavity wall is filled with other construction material based on its usage. In short, the thickness of the wall would affect the dead load onto the lintel, which indicates that greater size of lintel would be required.

4. You may refer to masonry design requirement, however the country I worked in does not even bother about it. Up to my knowledge, workmanship plays an important role in masonry. Besides, material wise, the strength of bricks is required to do load test frequently to ensure that it is up to allowable strength. However, when required, pipe sleeve installed in brick wall can serve the purpose too.

In case nobody else answers I have found this in UK Building Regs A - Structure.

Limiting penetrations without additional structural support to 0.1 m2 at 2 m centres seems like a reasonable enough rule of thumb.