All of these factors can affect the price of labor and its availability.
Economic conditions can affect the availability of labor and, thereby, can affect its price. When economic times are good, more people will have jobs. This means that there will be fewer people available to take any job openings. When the supply of labor goes down, the price of labor will (all other things being equal) go up.
Government policies can affect the price and the availability of labor. One clear example of this is the minimum wage. This is a policy that, paradoxically, increases both the price and the availability of labor. It artificially increases the price of labor and thereby makes more people want work.
Immigration clearly impacts the availability of labor. When large numbers of immigrants enter the country, they also enter the labor force and increase the availability of labor. When the supply of labor increases, the price of labor will (all other things being equal) go down. This is one reason some people want to reduce immigration (particularly illegal immigration). They feel that immigrants with low skills flood the market and drive down prices for low-skilled citizens.
Thus, all of these factors can affect the labor market.