Suggested answer:
(1) Overlook* is the most popular of the two, with 145 hits (one of which is a noun, overlooker).

(2) Only oversee may take on the meaning of "supervise"; an example from the corpus is the following:
...where my father is overseeing an experimental colony of tent caterpillars...

(3) No, only overlook takes on the meaning of "failing to take into account" or "ignoring"; an example from the corpus is the following:
The town tried to overlook her bohemian ways, for she was, after all, one of them.

Oversee seems to be strongly associated with the meaning of "supervising" or "managing".

(4) The two verbs may be confused because they are composed of similar parts, i.e. both have the prefix over- followed by a verb of visual perception, i.e. "see" and "look". Nevertheless, the two verbs have been shown to have quite distinct meanings.

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