I always like to remind people that music theory is not so much a set of rules, as many are often taught, but an explanation of what is happening and a language to discuss it.
My answers to those would be "probably not", "maybe", and "probably"/"yes"/"it doesn't matter" (screaming Strat/bebop Sax/ambient Frippertronics), respectively.
The common tones between two chords may not be enough to justify a substitution.
For instance, if you were to choose to substitute iii for I, then you will want to pay attention to whether or not the tonic is in the melody since that is the one note that is not shared between the two chords.
There are a few things that I would mention to look for while choosing substitutions though.
The idea of substitution, at least in the traditional sense, is that different chords fulfill a function within your composition and that you can choose other chords that will fulfill the same or a similar function.