You don't say what aircraft, but I imagine .76 is the turbulent air penetration speed. This is the speed the manufacturer says will give the best protection during turbulence, and when I say protection I mean between Mcrit and stick shaker. For the B757 we work on .78, it reduces gust loads on the airframe and can smooth out the ride for the pax.
The selecting of TAI above +10 has the effect of switching on the ignitors, or it may be because they think it will be required and gives them one less thing to think about. Try asking them next time they do it.
For the TAI on the B757 its when the aircraft is in cloud (vis 1 statute mile or less)or visible moisture and the TAT is above +10c and the OAT is above -40c (the lower oat limit does not apply when the thrust leavers are at idle)
Stand to be corrected on any of the above.