First, we don't observe individual stars that are 1 billion light years away (i.e. starlight emitted 1 billion years ago). Individual stars we observe are either supernovae which may be outside our galaxy but they are bright enough and visible for a short moment of time only; or stars in our galaxy, the Milky Way, which are at most 200,000 light years away from us.
The more distant objects we observe are whole galaxies – different from our galaxy. Quasars – visually "quasistellar objects" which are actually active galactic nuclei – are usually even further than that.
An object that is 1 billion light years away does get redshifted by Hubble's law. Hubble's constant is about 22 km/s per million of light years so 1,000 million light years gives them speeds of order 22,000 km/s, or 1/14 of the speed of light. This is surely a significant, observable redshift. The frequencies get lowered by the factor of $15/14$, too. It's not "quite" a coincidence that the number 14 is the age of the Universe in billions of years although you can't use this formula if you want a great accuracy.
Electromagnetic waves in the vacuum proceed indefinitely and they don't lose any energy whatsoever – except for the loss of the energy (and frequency) of photons described in the previous paragraph and (one more multiplicative factor of the same size, $14/15$) the decrease of the number of photons we collect each second.
The energy of the electromagnetic waves in the vacuum can't be lost due to the energy conservation: there's just nothing in the vacuum where the energy could go and it's easy to see that the precise, undamped waves are solutions to Maxwell's equations of electromagnetism. An even more obvious point is that the frequency can't change at all (except for the Doppler shift due to the relative speed, either due to Hubble's expansion or some extra velocity or due to different gravitational potentials in general relativity). Why it cannot change at all? Because if the electromagnetic waves are created by some process (acceleration of charges) that has some frequency, the "input" perturbations are periodic functions of time with the period $\Delta t = 2\pi/f$ which implies that all of their implications – such as waves measured a billion years ago – must be periodic with the same period, too. The frequency just can't get changed.
The total energy from a star or a similar localized source gets distributed to a surface $4\pi R^2$, the surface of the sphere, where $R$ is the distance. So indeed, how much light from a star we may see is decreasing as $1/R^2$. However, the angular (apparent) size of the star is also decreasing as $1/R^2$ which means that the density of energy (light) per unit solid angle is actually independent of the distance $R$. Stars that are further look "smaller" but the "intrinsic color" of the dot doesn't depend on the distance.