Any is liable to ambiguity unless it is used with care. "Any of them" may be either singular or plural. "It is not intended for any machine" may mean "There is no machine for which it is intended," or "It is not intended for every machine, but only for a special type."
Anybody else's, idiomatic and correct.
Anyhow, bad, do not use it.
Apparently is used of what seems to be real but may not be so. It should not be confused with evidently which is used of what both seems to be and is real.
Appear is physical in its meaning and should be distinguished from seem which expresses a mental experience. "The forest appears to be impenetrable," "This does not seem to me to be right."
Apt means "skilful" and should never be used in place of likely or liable. It also means "having a natural tendency."
As should not be used as a causal conjunction, e. g., "Do not expect me as I am too uncertain of my time." The word as stands here as a contraction of inasmuch. Substitute a semicolon, or make two sentences.
As to is redundant in such expressions as "As to how far we can trust him I cannot say."
At is often incorrectly used for in, e. g., "He lives at Chicago." It is also improperly used in such expressions as "Where is he at?"
As that should not be used for that alone. Do not say "So as that such and such a thing may happen."