Here are some basic facts:
Define discrete Fourier transform of a series of $N$ points $x_n$ as
$$X_k = \frac{1}{N}\sum_{n=0}^{N-1} x_n \exp^{-i 2 \pi n x k / N}$$
We get N unique frequency bins at frequencies $k/N$ were k runs from 0 to $N-1$. If the actual time of the series is $T$ then the width of the frequency bins is $1/T$, and the highest frequency bin is $(N-1)/T$.
If the signal you're measuring is real then $X_k = X_{N-k}^*$.
Ok, now let's get to your questions.
Suppose we measure a 2 Hz complex sinusoid for 1 second, with 20 points. Then the 2nd bin (numbering from zero) will be nonzero, but all the others will be zero. This is all nice and neat because 2 Hz fits exactly into the 1 second measurement window, eg. exactly 2 oscillations.
Now what happens if we measure a signal at 12.2 Hz? In this case the signal sits at a frequency that is between two frequency bins. What happens is essentially that the power shows up mostly in the 12Hz bin, but "leaks" into neighboring bins as well. This is illustrated in the figure below. There we plot the computed Fourier coefficients (blue dots) and the expected result of the DFT that I computed by doing the sum explicitly (red lines).
You can see that most of the power is at bin number 12, but there is also significant power in the neighboring bins. This power in the "wrong" place is called "spectral leakage." In this sense, having too coarse a set of bins does lead to loss of information because you can't tell whether the power in bins 11 and 13 are from leakage or from actual tones. One thing that affects the particulars of how spectral power leaks into neighboring bins is the window you use in the DFT. This is a rich topic and there's too much for me to describe here, but if you search the 'net for "fourier transform window" you'll find what you need.
Now going back to the list of facts I put forth in the beginning you can see that if we had simply measured for longer we'd have a finer set of bins and at least partially mitigated this problem. If you do this by zero padding you do get more points, and therefore finer frequency bins, but as you already said you don't actually have any more information because these zero padded points are completely made up. How do you reconcile that with the fact that you have more frequency bins? It all fits together when we realize that zero padding is essentially interpolation in the frequency domain.
One more thing. If all you care about is the total power then spectral leakage isn't much of a problem. When power leaks out of one bin into the neighboring ones the total power doesn't change much, if at all.$^{[a]}$ The only time you have to worry about spectral leakage messing up the total power in the DFT is at the very lowest frequency bins. If you need details on this I can provide. Just ask.
$[a]$: The details of whether it's precisely conserved are actually a lot more complicated than other people may have you believe. Watch out for people who cite Perseval's theorem too readily.
