It depends. As AlanT222 suggests, she needs to fill out a W4 and submit to her employer to begin to withhold taxes from her paycheck. For your convenience, please download this W4. This form has complete instructions on filling out the form as will as a worksheet to help determine how much tax to withhold.
She can file jointly or separately. Usually it is more advantageous to file jointly but be applicable in this situation.
No, she cannot hold her company liable for taxes not being withheld. She just needs to submit the W4 as soon as possible so she won't have a tax burden again next year. Be sure to click on the W4 link I have enclosed above to avoid any unnecessary delays.
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