1. on the one hand...on the other (hand)...中第一个 the 能不能省略？

答：不能省略。《朗文当代高级英语词典》有hand词条有如下说明：

Do not say “on one hand”. Say “on the one hand”.

不要说 on one hand，而要说 on the one hand。

2. on the one hand...on the other (hand)...和for one thing...for another...有没有区别？

答：有区别。说明如下：

A. on the one hand...on the other (hand)... = 一方面……另一方面……：用于引出两个不同的或是相反的观点或看法。请注意体会：

(1) On the one hand this job doesn’t pay very much, but on the other (hand) I can’t get another one. 从一方面来说这份工作工资不高，但另一方面我又找不到另外的工作。

(2) On the one hand the hotel is near the sea, but on the other hand it costs a lot. 好的方面是这旅馆靠海，可是另一方面房租太贵。

(3) On the one hand, he is very intelligent, but on the other hand, he does not work very hard.  从一方面讲他很聪明，但从另一方面来讲，他工作不是很努力。

(4) On the one hand, he works awfully slow, but on the other hand, he does nice careful work.  一方面他干活很慢, 但另一方面他的活干得非常仔细。

(5) On the one hand I’d like a job which pays more, but on the other hand I enjoy the work I’m doing at the moment.  一方面我想要一份薪水更高的工作，但另一方面我也喜欢现在的工作。

B. for one thing...for another... = 一来……二来……：用于说明某事的原因或理由（不存在不同与相反的意味）。请注意体会：

(1) For one thing, I’ve no money; and for another I’m too busy. 一来我没钱，二来我太忙。

(2) For one thing, he drinks; for another, he likes gambling. 一则他酗酒，二则他喜欢赌博。

(3) For one thing she is well educated; for another she is pretty. 她一则有教养，再则又漂亮。

(4) I’m sorry I can’t help you. For one thing (ie As a first reason) I’m in a hurry, and for another I have a bad back. 对不起，我帮不了忙。 一来我有急事，二来我后背有毛病。

(5) He couldn’t bring himself to say what he thought. For one thing, she seldom stopped to listen. For another , he doubted that he could make himself clear. 他无法表达自己的想法，一个原因是因为她很少会停下来听他讲，另一个原因是他认为自己可能说不清楚。