Main differences to take into account between continuous and discrete time signals
In general I'd say that you understand the differences pretty well.


You nailed the first difference- continuous time vs. discrete time (samples).
You were also correct about there being sets of indistinguishable frequencies in the discrete realm.  A corollary of this is that all discrete signals are band-limited, whereas continuous signals do not have to be.  This concept is most often referred to as the Nyquist frequency.
I don't entirely agree with your point about periodicity, though I believe I understand what you're getting at.  If by periodicity you mean having the exact same values repeated, then yes, a discrete period would have to be an integer number of samples.  On the other hand, if you take periodic to mean that the "underlying" signal repeats, then it is possible to have the samples not be the exact same if the period is not an integer multiple of samples.  You could still detect the periodicity with an autocorrelation though.  Anyway, if this point is confusing, don't worry about it- it's not terribly important.


It is, by the way, possible to view discrete signals as a special case of continuous signals.  You can model discrete signals as continuous signals that have been multiplied by an infinite set of evenly spaced delta functions.  If the delta functions are separated by $T_s$ seconds, then in the frequency domain they can be represented by another set of delta functions that are separated by $\frac{1}{T_s}$ Hz.  The multiplication in the time domain is equivalent to convolution in the frequency domain, so copies of the signal are reproduced in the frequency domain at each of the delta functions.

Though the mathematicians in the audience will probably scream at me for saying this, I think that you can likewise look at continuous signals as a special case of discrete signals, where we take the limit of $T_s$ as it approaches zero.