هبة (Heba) is a female name that means 'gift'.
I'll try to comment on the translation later - no time now...

هادية does not mean "gift", but the name you have suggested "هدى" does not mean gift either. However, هادية could mean the one who presents the gift.

English term (edited): Proofreading

But the Arabic reads like machine translation. There is no way to proofread it here, for several reasons:

1. There is no way to tell what the message is.

2. The amount of surgery required is staggering for such a small piece.

3. The proofreading is a separate question, not related to the question about the word "gift."

4. Proofreading an Arabic text would be an Arabic-Arabic question, not an English-Arabic question.

5. It would be better to post it as a Russian-Arabic question if you have the Russian text.

6. KudoZ is primarily a service about single, concrete linguistic issues, like terms and grammar questions. Proofreading a text, especially one that involves multiple errors, goes far beyond KudoZ purpose. You should consider posting a request for a volunteer linguist to help you with this matter outside of KudoZ. You can post your request on the JobZ page in ProZ.com.