Homepage Menu Not Syncing With Back End

Hello, I have two issues with the homepage menu. 1. How I have it set up on the back end does not match how it looks on the site, it's not reflecting the right order. 2. I've deleted a page which is still showing up, and added a category which is not showing up. Images: Some of the images, even after resizing are not showing up the correct size. Font: Is there a way to change the font? I downloaded a plug in that changes the font, but it changes the paragraph copy, versus just the headlines. I would like to just change the headers. Thank you greatly for any help!