1: I believe the purpose of this is to account for alternative methods of pipe fastening. Imagine the ends of two mating pipes having a circumferential portion channeled out, and a dresser coupling fitting inside that groove.

2: You must always consider mechanical allowance unless you have evidence that the deficiency permitted by the mechanical allowance simply doesn't exist. If you order stock A106B SCH 40, and the mill tolerance is 12.5%, then the mill is promising to sell you something that doesn't have a deficiency greater than 12.5% at some part of it. However, if inspection reveals that you do not have 12.5%, such as if the purchaser required something tighter, then you are justified to ignore the tolerance.

However, that doesn't get you out of corrosion and erosion allowance(s), if any, but the end user decides what those allowances are, even if 0.

Note that all components need to meet code requirements, so you'll want to look at elbows, too, and not just pipe.

3. 3a and b offers two ways to calculation design thickness, the latter of which uses an ID that's been pushed out to consider tolerances and allowances. Both are "just" stress calculations.

Minimum required thickness, tm, requires you to put those allowances in when you select a pipe for purchase.