Not exactly. A BH is the left over remnant of a large star after catastrophic collapse of the core after the star goes supernova. The same applies toWhite Dwarf stars, Neutron stars and Pulsars...they are in effect all stellar remnants after a star has used up its available hydrogen.
Spiral arms in galaxies are essentially created due to the galaxy's rotation. They are actually density waves where stars pile up, similar to a traffic jam. Stars are moving through these density regions all the time, and also exist in between the spiral/density arms.
As a conglomeration of gas collapses under gravity, the core will start to heat up and eventually some limited fusion starts. This is known as a proto star until finally full fusion gets under way and we have the formation of a star. Examples of proto star and stellar formation processes, are seen in the Eagle nbula and Orion, just to name two.
Planetary formation follows with clumping in the accretion disk and dust etc that surrounds the newly formed star.
The first stars are known as GEN1 stars because they were the first to form, and POP3 stars due to their total lack of metalicity, forming solely from H and He.
Obviously!