1. The latter "Он не знает моего имени" is grammatically more correct, however the former one "Он не знает моё имя" is so widely used, that became universally acceptable. In everyday speech more people will use the second than the first. 2. "Does много always make the verb neuter?" Seems so. "Здесь было много воды" (f) "Здесь было много воздуха" (m). "Здесь было много {put anything here and it will still be grammatically correct}" 3. "У меня много опыта. У меня есть опыт в Китае. Why isn't it опытa used in the second phrase since it is also genitive case?" No, it's not. It is a nominative case. The nominative case answers the questions "who?" or "what?" I have (what?) experience in China.

Он не знает моё имя和 Он не знает моего имени 这两句话都是对的，前者更口语化一些。 Здесь было много воды。这是个无人称句，句中的谓语过去式用中性，现在时用第三人称单数。У меня много опыта.这里много 用作不定量数词时要与名词二格连用，表示很多经验。У меня есть опыт в Китае，这里У меня есть что 这是固定句型。

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