How does an accreting black hole acquire magnetic fields?
Addressing (2) and (3) first:

In a case like this, your best option is to go straight to the source. In this case, that would be Blandford &amp; Znajek (1977), the originators of the proposed mechanism. they have several figures regarding different magnetospheric structures depending on different magnetic fields. However, the most important one is Figure 1, the general case:



$D$ represents the accretion disk, while $T$ is the transition zone where matter is rapidly moving radially towards the black hole. The lines represent magnetic field lines, along which charged particles. Electrons (e-) travel in the direction of the medium arrows on each field line; positrons (e+) travel in the other direction. The field lines are closer together in the disk area closer to the black hole, indicating the stronger magnetic field.

If you want a good overview of the process, this is the paper to look at. That said, it is far from an easy read.

Regarding (1), I'm not an astronomer and not really qualified to tell you what the mainstream opinion among astronomers is. However, as far as I'm aware, the Blandford-Znajek process is currently accepted as a strong possibility for generating the magnetic fields observed near most black holes (including stellar-mass black holes).