Mobil. Mobil 1 is a family of synthetic lubricants produced by ExxonMobil.
Doubtful. Typically, the lubricants are developed with an additive supplier, like Infineum, Lubrizol, Afton...etc, who know more about lubricant design, additives and their behaviours than any car company on the planet.
How much oil flows is determined by the oil pump, not the filter. Most oil pumps are positive displacement, which means that, unless the relief is engaged, they displace the same amount of oil, which then goes through the filter, with every rotation.
Toyota also doesn't produce oil filters, they are produced by several different companies, depending on the application. Toyota also sell "fancy aftermarket" filters with higher efficiency ratings through TRD, FWIW.