There is a sentence like the below.

• I really didn't want to add another talent for people to envy me for.

What I want to ask is whether the above sentence is right or wrong without 'for.'

And also in the next sentence, is that sentence still possible without 'to'?

• So for someone I send a gift to I put a couple week of notice but for another person I just want to call I only have to put a day or two.

cf. "envy" and "send" are both ditranstive verbs.

ie, next sentences are possible.

• I envied him his good looks.
• I envy you having such a close family.
• I sent my daddy a present.

So I'm asking you the two questions.
I'm expecting your opinion.
Thanks in advance.

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Both for and to are required. Personally, I would accept the second one without the to, but I don't think most people would. The "rule" is that you have to have the preposition in the subordinate clause when the object of that preposition is being relativized.
talent for people to envy me for (talent)

someone I send a gift to (someone)

>when the object of that preposition is being relativized.
Care to translate, CJ? Thanks.
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Thanks, Calif Jim & Marius Hancu.
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Marius Hancurelativized.
Care to translate, CJ?
As in the examples. The noun at the beginning of each example is 'being relativized". These are the antecedents of the gaps at the end of the expressions where the same word would go after the preposition.
Did I get the word wrong? Maybe I did! But it seems to me I've read that word in linguistics books with that meaning. Who knows? I may have misremembered it. Emotion: smile