Implement an advanced search in a team site with site owner permissions, no server access and no sharepoint designer.

I am in the way to create a search interface to search document in the team site. how do I go for this?

I read about basic search center? enterprise search center and fast search center. can basic search center help me here? if yes how to do it as I have tried the way to set a basic search center like seen in tutorials but got a basic search center without a search box  field?

Also, When searching in the default library search box I keep getting  in my result links to old documents that have already been deleted from the library. It is this normal?

Does this default out of box  library search box enough for me to do a search in the libraries of the team site?

What do I need to implement an advanced search in a team site which will search only in the libraries of the team site?

I am a site owner with no access to server and no right to use SharePoint designer.

Thanks.