Yes, if you have a net recognized loss. Your recognized loss/gain is treated similarly to stock or investments. It is netted with other capital gain/loss and taxed according to long- or short-term gain loss. Here is a link with some information about how cryptocurrency is taxed. At the bottom of that FAQ there are more FAQs with details on how to report it on your tax return.
Yes they can. Whenever your total capital gains and losses for the year add up to a negative number, you incur a net capital loss. If the net capital loss is less than or equal to $3,000 ($1,500 if you are married and filing a separate tax return), then that entire capital loss can be used to offset other types of income--like the income from your job. If your losses exceed $3,000, then the amount over $3,000 will be rolled forward to the next tax year.
For traders on multiple exchanges with many trades, using one of TurboTax's cryptocurrency partners can make the reporting process much simpler.