Is there any limit on how deep the Server Owner can access my data? this is my first post on DBA. I'd like to get some clear ideas from you.
First of all, this may sound as a discussion but it's not a debate. 
What I'm looking for could be something like "Yes, they can do whatever they want" or "No, no way!"

Recently I've finished developed a web application. Once it's done I was told to contact Server Area department so they could help me out with uploading my SQL db, grant permissions, etc etc.

So, I did that.
They explained how they were used to work and we agreed on uploading a non-operational version db, so we could test permissions etc. They told me to handle them a back up of the db. They would restore it.
First thing making noise within me. Shouldnt I be the one restoring back ups? "Well.. I'm no dba yet, I'm sure they know better." was my answer to myself since those could be their practices.

Two days later they send me an email, saying the backup is up and giving some suggestions.
They needed my db tables to be normalized and have the proper indexes.

My reaction wasn't sweet. First of all, we both had talked about it and the back up wasnt not the operational one... So, are any conclusions relevant?... and bay the way, tables are all fully normalized. Second, is it ok for them to access that deep? What if the information contained in my db is critical?

Thanks a lot, hope for some insights on this matter.
From what I gather in your post, you are on the development side and they are on the administration side.  I can see why they would like to handle the administration portion of the database(s).  That would most definitely include backup/restore, security, etc.  If they are responsible for the maintenance and administration of the data layer, then that is more than appropriate.

As for their suggestions about data normalization, there is a possibility there suggestions are prudent.  At the same time, that would be a database design/development decision which sounds more like your responsibility.  Maybe they were just friendly suggestions, that's up to you to decide.  But if they were forceful "recommendations" then that would be another story, as you application is likely to adhere to the schema.

As for the restore on a development server, it is very shop-specific.  The overruling argument will be who had jurisdiction on that particular server (or servers).  Again, this is very shop-specific.

What I'm trying to get at is there are too many variables, and as participants of DBA.SE there is really no way we can give you sound advice.  I recommend you take this argument to management in your company that can make a decision one way or another.