The superconducting state of an optimally doped single crystal of Ba(Fe0.93Co0.07)2As2 was investigated by 75As NMR in high magnetic fields from 6.4 to 28 T. It was found that the Knight shift is least affected by vortex supercurrents in high magnetic fields H\u3e11 T, revealing slow, possibly higher order than linear, increase with temperature at T≲0.5Tc, with Tc≈23 K. This is consistent with the extended s-wave state with A1g symmetry, but the precise details of the gap structure are harder to resolve. Measurements of the NMR spin-spin relaxation time T2 indicate a strong indirect exchange interaction at all temperatures. Below the superconducting transition temperature, abrupt changes in vortex dynamics lead to an anomalous dip in T2, consistent with vortex freezing from which we obtain the vortex phase diagram up to H=28 T
