@Veronica, is there a specific reason you are running it as a web application ? You lose some live functionality with a compiled web app vs. website, check documentation for the differences.
I use it as a website with Visual Studio 2013, spin it up by running it with Ctrl + F5 which runs that application without debugging, this way I can make full code changes. I hit the pages that I will be working on or the web parts etc. I make my changes to the code or markup and just reload them in the browser again, it will recompile just the pages you are touching and their respective web parts, code ,etc. It is much quicker. If you change the web.config or a library, or global code ever it will take a bit longer to compile when you refresh.
Additionally, when I send the site live or if I am working on a production site, I just mirror the entire website down on my development machine. Make the change and just send the pages, web parts, library or class back to the production server after I test it locally. I either just copy the enhancements, changes directly or I export and import such as with modules.
One other thing, it sounds like you are new to Kentico. I had the same uneasiness when I started using Kentico, years ago. The habit is to build your project, hit F5, and test. Back and forth, back and forth. With Kentico, you can still do that, but the project is so large the to run it every time is slow and takes a bit of time, minutes. I only run and debug the application when there is a problem or when I am finally done with changes. Do please read the documentation on website and web applications with Kentico.