You cannot do that because the verb form "were" is subjunctive mood for the verb "to be", meaning that the idea that "his address being of great importance" is hypothetical or imagined. "As if" introduces a hypothetical, but "like" does not. For that reason, "like" would not make sense. If you use like, you need to use the simple past tense: "It did not seem like the subject of his address was of great importance."

Yes you can do that. It would mean the same thing. You can also switch that bit for "as though" or "that" without changing the meaning.

If you did that, you would have to use 'was' in the second part of your statement to be grammatically correct. The meaning would still be hypothetical - just moving toward more certainty.