"Totally random" as distinct from "partially random?" Like pregnancy, randomity is categorically "total." It is all-or-nothing.
Randomity, by its very definition, indicates the absence of fixed aim or purpose. Synonyms include chance, stray, casual, fortuitous, accidental, aimless, haphazard. To suggest that randomity may be "partial," ie. that planning, intention, design, is involved, is to make it no longer randomity.
No, as distinct from locally random. For example, a certain region in the genome is particularly vulnerable to insertional mutations. But within that region, the insertion point is random.
In computers, we have something called pseudo-random with seed, which for all intents and purposes is random, but a statistical analysis of a large sample will eventually show non-randomness. Pure random is actually not too easy to achieve.