No, and this is one of the nut oils to be most careful with. The major brazil nut allergen Ber e 1 is a small 2S albumin that withstands roasting at 100C and resists digestion by pepsin, so it is not the kind of protein that processing quietly disposes of. Brazil nut oil is sold cold pressed and unrefined, which retains protein, and work on brazil nut lipids indicates the oil fraction itself acts as an adjuvant that strengthens the immune response to Ber e 1. Brazil nut allergy is also associated with severe reactions, so this is a question for an allergist and not for a home trial.

Only traces, despite the marketing. The selenium in a brazil nut is built into the seed protein as selenomethionine, and when selenium-rich oilseeds are pressed the mineral concentrates in the press cake while the oil is left with a small fraction of it. That means the oil sidesteps the reason nutritionists warn against eating brazil nuts by the handful, since selenosis comes from the nut, but it also means you cannot use the oil to top up selenium.

No. Brazil nuts grade D for nickel and C for both histamine content and histamine liberation, while the oil grades A on all three. Nickel binds to the mineral and protein fraction of the nut and does not follow the fat out of the press, and there is no histamine load in a pure lipid. For systemic nickel allergy or a low histamine protocol the oil is genuinely a different food from the nut, which is not something you can say about the allergy question.

Not well. It carries a large share of linoleic acid, so it smokes low, turns bitter and oxidises quickly under heat, and cooking destroys the sweet, faintly coconut-like aroma that is the reason to buy it. Use it cold over rice, roasted squash or a leafy salad, keep it sealed and cool, and replace it once it smells sharp rather than sweet.