1. I saved the following to a html file. I uploaded in the sever and with default encoding Greek, it was displayed correctly. I changed browser encoding to UTF8 and i got question marks.
That's understandable, only one of them will work. Just a question: is the text really in Greek language? I don't know what your nationality is so I don't know if you're saying Greek meaning "some rubbish characters" or if you're saying Greek because it really is and should be Greek alphabet. (No offence here, people call dummy fill-in text "Lorem ipsum" "Greek".)
If you want to work with UTF-8 you have to work with UTF-8 only - you can't have a part in iso-8859-7 (or what is it that you have) and part in UTF-8. There's no point in saving from notepad in anything else than UTF-8, all of your HTML pages must be saved in UTF-8 etc.
For testing if the SQL is in UTF you don't have to upload it to server. Just change the extension to .html, open the file locally in your browser, change browser encoding do UTF and see what you got.
A. To get the html code of all my pages, open it with notepad and encode it with utf8
B. To put the meta charset for utf8 to all of my pages. ( Have in mind that i did that for the pages that are used for the searching section, and also I did it with the combination of saving it with notepad in utf8 )
Well, you have to do both - all your files (that work with the UTF-8 content of your database) must both themselves be in UTF-8 and their meta charset must show that.