given the following sentence
I have a snake of which the head is white and (of which) the tail is black.
In this expression, can I omit the second (of which)? Or shouldn't I omit it?
To answer your question: yes, you could omit the second of which and get away with it.
However, this sentence is not very good to start off with; usually, when describing attributes of an object, you use adjectives or the preposition with.
I have a sneak with a white head and a black tail.
I have a white-headed and black-tailed sneak.
The first alternative—using with—is more idiomatic.
Yes, given that the conjunction "and" can be taken to subject the next phrase to the first "of which." And if the parentheses are original, they themselves are a clue because all that go between parentheses can always be dropped without harming the structure of a sentence (even though harming its meaning, as just in this parenthesized phrase!;).