Can I control solid state relay directly from arduino digital pin?
According to the datasheet there are multiple models.
Some already have an input resistor for the led (in the opto-isolator) inside the package, but some don't. For the ones that don't have a resistor inside, you'd need to add one yourself, to limit the current to around 10mA.
Some models also have a snubber circuit inside the package. The need for this depends on what kind of load is connected (inductive vs. resistive (AFAIK)).
I thinks the green thing, in the picture, is a fuse. On the other side of the SSR you can see and indicator led, transistor, and 3 resistor (one to limit current to the SSR, one to limit the current through the indicator led, and on for the base of the transistor.). They probably use a transistor, because the current for the SSR and the indicator led combined, is to high for certain micro controllers.