If a question is deleted or in other words isn't visible for users, then who will vote to undelete that question since its not visible/accessible to common users?.
Anyone who has at least 10,000 reputation on Super User will be able to see deleted questions, and can vote to undelete them if they so wish, as long as the question hasn't been locked through deletion by either an elected mod (a user with a diamond next to their name), or the Community User.
When I make use of my vote to undelete, some kind of "signal" is emmited to moderators or other privileged users in form of an advise/popup about an user wants to undelete a question?.
(same as question nº2 but in other words) Moderators has advises of undeletes and they revises undelete requests?. At least moderators will know that an user has requested an undelete?.
I'm not 100% sure what happens when you try to undelete your own question. If you deleted it yourself, I think you might be able to just undelete it yourself (not sure though).
If other non-mod users voted to delete your question, and it was deleted, then it will take 3 undelete votes or a single undelete vote from a mod to undelete your question. Undelete votes can be seen globally across the entire site by users with at least 10,000 reputation, so if someone casts an undelete vote on a question, then these users will know about it.
However, once again, if the question was deleted by an elected mod or the Community User, then the question is "locked", and can only be undeleted by a mod.
An user really could have hope/chance to see his deleted question undeleted?.
If the community thinks that your question has value, then yes, it has a chance of being undeleted. Otherwise, no.
If a question is deleted, it is allowed to publish a new question with the same (fixed) content?. that is what I should do?.
There's a reason your question was deleted. It probably did not meet the standards of the Super User community. Posting the exact same question again probably isn't going to do you any good. If you think you can post a new version of the question that would meet community standards, then you could probably try that with better results.
If your question was completely off-topic for the site to begin with, however, then you shouldn't repost it if any version of the question that you could come up with would still be off-topic.
It is allowed to use the chat to "spam" requesting for an undelete of a question?. Is there a place on S.E. to request this, more than the usage of the "undelete" button?.
I don't see how "spamming" anything in any venue here would be welcome, by anyone. You could probably ask very politely once if users want to undelete your question, but you should be prepared for a polite but firm No, in the best case.
Why some deleted questions has an additional "reopen" option while other questions only have the "undelete" option?.
Questions that have a status of "On Hold" or "Closed" can no longer be answered. Once they have one of those statuses, users can vote to re-open them for answering if the questions meet community standards, such as through editing, for example.
This is different from deletion. A question can be closed, but can remain on the site until a mod or a group of users votes to delete it. Once a question is deleted, it cannot be reopened until it is undeleted first.