You can make your logo have a px size instead of a percentage based size. In "Customize" -> "Site Title" -> "Site Title":
Screen Shot 2016-03-28 at 10.52.02.png
Some images look fuzzy/ blurry when they load, with some of those flickering and then turning sharp, after a few seconds, while others just stay fuzzy.
When you open an image in the lightbox it first shows a lowres image and then loads the highres version. That's how I coded it. If your image doesn't turn sharp it probably means that you need to upload a larger version of that image.
Your third question, I don't understand what you mean, can u give me a screenshot?
Your other questions:
Atm it's only possible to have one menu.
What you mean is you want some kind of filter functionality. Right now theres no filter functionality, but for each category you'd need to create a page that contains all the project thumbnails of that category.
On the about page you could hide your menu points by using custom css. Please take a look here at "Menu Color based on current page": http://laytheme.com/documentation.html#custom-css-styling
Just instead of changing your menu color on a specific page, you would hide menupoints on that page. You'd need to know some basic css to do that.