I am going to use CKEditor to format the text while editing the content of my website. The content is saved into MySQL database, so if I use CKEditor, will the text be saved with its formats (size, color, etc) and displayed with that format in client side?
Yes CK editor will save the way you specify. On CK editor you have a source button if you click on it you will get the html source.
Yes and no. Not really.
Some information will be saved, yes, but some other will require the CSS of the editor page and the display page to match. They usually do, but not necessarily.
CKeditor offers several ways of customizing the HTML that's being generated. Your best option would be to use CSS classes for SPAN and DIVs, and all other tags you allow in the editor; then, define those in a separated .css file that would be imported by your CKeditor edit page as well as the site at large. This will give you as much WYSIWYG as you're going to get.
(I'll try and whip up an example later when I get access to a CKeditor on my servers; but you can also looks at CKeditor' documentation).