Yes. For best results, wrap it well with cling film, then put it in a Ziplock bag or wrap it again with foil and store it in the freezer (usually for up to 6 months, though this dependes on the temperature of your freezer).
Yes, you can. You might consider portioning the spinach for future smoothies as you put it in the freezer (like in multiple plastic bags) so that it's easier to take...
These are most likely caterpillars or other pests. Consider investing in pesticides or other organic forms of pest control. Some plants like basil and garlic are known to repel some...