I am deducting the medical fees I paid for my mother, who is 78 and living in her own home, with my itemized medical expenses (I qualify to do this). I’m 55 years old. For 2013, do I apply the 10%- or 7.5%-of-adjusted-gross-income threshold?

Because you are not at least 65 years old by the end of the year, you apply the 10% threshold to all of your itemized medical costs (which include costs related to your mother). If she claimed them on her own return, she could apply the 7.5% threshold.