H-1B itself, with the Trump reforms, should become an immigrant visa (i.e., Green Card) instead of a temporary worker visa. H-1B workers should be able to transfer jobs or quit in a huff if they don't like the working conditions, without being kicked out of the country. Social assistance, however, should not be provided until a number of working years have elapsed - until then, only a free ticket home for the rare tech worker who falls into indigence.
H-1B's allow for anchor babies only, they don't let you bring in relatives except under the 6-month tourist visa.
Family members of the H-1B worker are admitted to the United States in the H-4 category. Qualifying family members include only the spouse and unmarried children under 21 years old. As of may 2015, they too can work.
As long as you hold a valid H1B, then you’re eligible to adjust your status to green card holder.
H1bs can change jobs. The “h1 transfer” is a new petition without restriction of the h1b cap.