it seems that这里that引导的表语从句可以省略that吗？

   【答】可以。如：It seems (that) you were lying. 你刚才好像在撒谎。（摘自《薄冰英语惯用法词典》p.909）

    it seems happy that 这里that引导的主语从句可以省略that吗？

   【答】可以。

    it seems to me that这里that引导的表语从句可以省略that吗？

   【答】可以。如：it seems to sb (that) 在某人看来[用于发表对某事的看法时]： It seems to me you don't have much choice. 我觉得你没有多少选择的余地。（摘自《朗文当代高级英语辞典》第六版）