Relationship between the carrier frequency and the propagation distance?
Even in vacuum, there exists an attenuation that is inversely proportional to the frequency squared of the signal. It is called the free-space loss.

The ratio of received power vs. transmitted power (for polarization-matched antennas aligned for maximum directional radiation and reception) reduces to:

$$
P_r / P_t = (c/(4\pi ~d ~f))^2 ~G_{0t}~G_{0r}         ~~~~~~~~~~~~~[1]
$$

where $c$ is the speed of light in vacuum ($\approx3\times10^8 ~$m/s), $d$ is the separation between antennas (in meters), $f$ is the central frequency (in Hz) of the signal, and $G_{0t}$, $G_{0r}$ are the antenna gains under the conditions stated above.

As can be seen from Eq. [1], for a specific power ratio (attenuation), there is a fixed relation between the frequency and the propagation distance.

Equation [1] is a particular case of the well known Friis transmission equation. The term $(c/(4\pi ~d ~f))^2$ is called the free-space loss factor, and it takes into account the losses due to the spherical spreading of the energy by the antenna.

See, for example, the following reference for further details:

C. A. Balanis, "Antenna Theory. Analysis and design", 2nd edition, 1997. (Section 2.17, Chapter 2)

The inverse relationship between distance and frequency is not due to the propagation phenomenon itself, but due to the physical dimensions of the receiver antenna (which does depend on frequency, in something called the effective area of the antenna). In practice we always have an antenna matched to the desired frequency, and thus we have a propagation distance limited by this restriction. 

Regarding the second part of your question, normally a carrier signal is added (for example, in AM modulation) for simpler detection circuits. Besides, the carrier signal is used sometimes to perform synchronization at the receiver. I have not seen before the use of a carrier to "strengthen" the message signal.

Actually, instead of using an extra power to transmit a carrier, it can be used to increase the power of the message signal, and thus let the message travel a longer distance with the same attenuation.