I've worked specifically with CKEditor before, to the complete and utter satisfaction of my employer. I've accomplished this by extremely high-quality communication, which is often a big problem when hiring freelancers. To ensure that I am going to do exactly what you what, I will reformulate what you want done, so that we both have a perfect clarity about what I will do for you. Please correct me if this is in any way inaccurate. Here is my reformulation:
1) CSS
a) Styling: Currently, the CKEditor uses its own internal styles when editing. I will adjust it to apply only the styles of the original page to the edited text.
b) Menu: Currently, the CKEditor styles menu displays its own style names. I will change it to only include styles defined in the linked CSS file
2) Images
Currently, the user can only specify an image that is already online. I will make it so that the user can upload pictures from his own computer. There are two ways to do this:
a) Upload them to your own site. You will have to store their files. In this case, you should probably impose some limitations on how large the files should be
b) Upload them to an online image hosting service like Imgur
Please specify which way you'd like to do this.
3) Browser compatibility
You would like this to work on all browsers. However, since you haven't provided many details on this nor a link to the page in question, I don't really know what exactly I'll have to do.
Sincerely,
Matthew