Growing crops on the Moon
Plants are adapted to the conditions we have here on earth, therefore, for them to grow on the moon we would have to recreate the conditions found on earth (or at least find conditions that we can create and they can grow in). To do this we would need to replicate climate (temperature, air pressure, humidty etc.), provide (sun)light at the necessary intervals and intensity, provide water, air, and nutrients of the right composition, intervals and intensity. That is a simplified version... 

In reality there is great variation in how plants require these things. Some cope with long dark periods better than others, some cope with drought better than others, some cope with chemical variation in the soil better than others so answering this question is hard. But generally growing plants on the moon will require the ability to recreate (to some degree depending on the sensitivity of the plant) the conditions a plant has evolved under on earth.

Thus to answer your questions: 

Length of day can have strong effects on growth patterns, two weeks of darkness is likely to be a major upset for plants! Just transplanting plants of the same species from different latitudes can affect the growth patterns because of changes in length of day. Try putting some plants in darkness for two weeks and see what happens.

Plants all vary in their ability to meet the requirements of space growth. There will only be a short list of plants that could with "small" modifications to the moon's environment, the more we adapt (adding artificial light, watering, adding nutrients etc) the longer that list would become - the limitation is in our ability to adapt the moon.

See above for reasons why plants might struggle. Oh and we would need to consider the effects of reduced gravity too...

Here's a little something from nasa about how plants are used in space vehicles. And another on light and gravity.