When to use 是 with 当中， 过程中。
To answer your first question, yes, 在所有的礼当中 and 在所有的礼中 mean the same.
For the second question, yes, you can use 是, but you change the sentence structure from the original one.  We understand the original one as: 在所有的礼当中，我/最喜欢/你送给我的/真丝手袋, where the main verb is 喜欢 and 你送给我的 is an attributive phrase modifying 真丝手袋.  The main part of the sentence is 我喜欢真丝手袋.
And for your sentence 在所有的礼中，我最喜欢的(礼物)是你送给我的真丝手袋。we understand it as: 我最喜欢的/礼物/是/你送给我的/真丝手袋。where the main verb is 是 and 我最喜欢的 and 你送给我的 are attributive phrases modifying 礼物 and 真丝手袋 respectively.  The main part of this sentence is 礼物是真丝手袋.
By the same token, both of these two sentences are correct but with different syntax.

在所有的首饰当中，我最喜欢这幅耳环。// among all the 首饰, I like this earring most.


在所有的首饰中，我最喜欢的是这幅耳环。// among all the 首饰, what I like most is this earring.

As for your last two sentences:

我最喜欢的名人是姚明，因为他在球比赛中的态度热情和谦虚。


我最喜欢的名人是姚明，因为他在球比赛中的态度是热情和谦虚。

Both are problematic.  The correct one can be:

我最喜欢的名人是姚明，因为他在篮球比赛中的态度是热情和谦虚的。

The reason why we need a 的 is that in Chinese(unlike in English) adjective can not modify noun directly and it should have a 的 to form an attributive phrase.  E. g.  we can say 热情的态度, 谦虚的态度, but not 热情态度, 谦虚态度. 热情 and 谦虚 are adjectives.
P. S. I feel 谦虚的态度 is natural, but 热情的态度 is a bit off in this context. 热情的态度 is natural when put in the service context. But it could be just me.