In a series circuit, how do these factors affect the current?

Is this a course you are taking? It is not normal to use lamps to teach basic principles because a lamp is not a reliable resistance. Normally this would be taught using resistors with fixed value, and then the operation of a lamp can be explained separately. Here is a free course in basic electronics: www.phy.davidson.edu/instrumentation/NEETS.htm

When two devices are hooked in series, the voltage has to divide, part across one device and part across the other. The same current flows through both of them. So if voltage is constant, then hooking lamps in series will decrease the current.

If voltage across a lamp is increased, the current also increases, but there is no exact relationship between voltage and current because the resistance of a (tungsten) lamp also depends on its temperature.

Different types of lamps have wildly varying characteristics.