An Amplitude Modulated (AM) wave is represented by the expression where a 10kHz sinusoidal message signal modulates a 1MHz carrier signal. The peak carrier amplitude is 10 V and the peak message amplitude is 6V.

Peak carrier amplitude, $A_c = 10 \text{ V}$.
Peak message amplitude, $A_m = 6 \text{ V}$.

The modulation index $m$ is given by the ratio of the peak message amplitude to the peak carrier amplitude.

The modulation index is $\boxed{0.6}$.

Message signal frequency, $f_m = 10 \text{ kHz} = 10 \times 10^3 \text{ Hz}$.
Carrier signal frequency, $f_c = 1 \text{ MHz} = 1 \times 10^6 \text{ Hz}$.

The USB frequency is the sum of the carrier frequency and the message frequency.

The LSB frequency is the difference between the carrier frequency and the message frequency.

The Upper Sideband frequency is $\boxed{1.01 \text{ MHz}}$ and the Lower Sideband frequency is $\boxed{0.99 \text{ MHz}}$.

Peak carrier amplitude, $A_c = 10 \text{ V}$.
Antenna resistance, $R = 50 \text{ } \Omega$.
Modulation index, $m = 0.6$.

The carrier power is given by $P_c = \frac{A_c^2}{2R}$.

The total transmitted power for an AM wave is given by $P_t = P_c \left(1 + \frac{m^2}{2}\right)$.

The total power transmitted is $\boxed{1.18 \text{ W}}$.