I would like to know if it's possible to bring back to life a post of mine (a question) which I deleted? If so - would the reputation I gained from it be restored?
Post deletion is "soft;" deleted questions and answers can be restored. Users with more than 10K reputation can vote to undelete questions and users with more than 20K reputation can also vote to undelete answers. Except when those posts were deleted by a moderator, in which case they can only be undeleted by a moderator.
If you've deleted one of your answers, you can easily restore it. When it comes to questions the situation is a bit trickier. You can't see your deleted questions in your profile (that's an abillity reserved for moderators), you can only see them if you have a direct link to them. Also, you can't delete your own question when it has an upvoted answer and you can't delete your own answer if it has been accepted.
When it comes to reputation, when a post is deleted all reputation changes are as if they never happened. Except if the post was deleted more than two months after it was posted and it had a score of at least 3. If that's the case, you keep all earned reputation. When a post is undeleted, all associated reputation changes are restored.