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If so, which ones are?

If not, is it known whether or not these are mutually exclusive?

Is there a page that exhaustively lists encryption systems and properties such as these? I could not find a resource to help me find these answers on my own.

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$\newcommand{\Enc}{\operatorname{Enc}}$ Actually, Pohlig-Hellman exhibits a homomorphism and commutativity.

For the commutativity, see poncho's answer on your other question.

The homomorphism goes as follows
(it is really just plain multiplication, not unlike what is possible with textbook RSA): $$\Enc(m_1)\cdot\Enc(m_2)=m_1^a\cdot m_2^a=(m_1m_2)^a=\Enc(m_1m_2)\pmod p$$

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