Website:
The Web Site project is compiled on the fly. You end up with a lot more DLL files, which can be a pain. It also gives problems when you have pages or controls in one directory that need to reference pages and controls in another directory since the other directory may not be compiled into the code yet. Another problem can be in publishing.
If Visual Studio isn't told to re-use the same names constantly, it will come up with new names for the DLL files generated by pages all the time. That can lead to having several close copies of DLL files containing the same class name,
which will generate plenty of errors. The Web Site project was introduced with Visual Studio 2005, but it has turned out not to be popular.
Web Application:
The Web Application Project was created as an add-in and now exists as part
of SP 1 for Visual Studio 2005. The main differences are the Web Application Project
was designed to work similarly to the Web projects that shipped with Visual Studio 2003. It will compile the application into a single DLL file at build
time. To update the project, it must be recompiled and the DLL file
published for changes to occur.
Another nice feature of the Web Application
project is it's much easier to exclude files from the project view. In the
Web Site project, each file that you exclude is renamed with an excluded
keyword in the filename. In the Web Application Project, the project just
keeps track of which files to include/exclude from the project view without
renaming them, making things much tidier.
Reference
The article ASP.NET 2.0 - Web Site vs Web Application project also gives reasons on why to use one and not the other. Here is an excerpt of it:
- You need to migrate large Visual Studio .NET 2003 applications to VS
2005? use the Web Application project.
- You want to open and edit any directory as a Web project without
creating a project file? use Web Site
project.
- You need to add pre-build and post-build steps during compilation?
use Web Application project.
- You need to build a Web application using multiple Web
projects? use the Web Application project.
- You want to generate one assembly for each page? use the Web Site project.
- You prefer dynamic compilation and working on pages without building
entire site on each page view? use Web
Site project.
- You prefer single-page code model to code-behind model? use Web Site
project.
Web Application Projects versus Web Site Projects (MSDN) explains the differences between the web site and web application projects. Also, it discusses the configuration to be made in Visual Studio.
1) It is possible to use SharePoint in a custom web app. They do have to be on the same machine, but you can do a lot by referencing the SharePoint dll. With the object model you can integrate certain aspects of SP into your app like document libraries for instance.
2) Using a custom MasterPages is very powerful. You can lean your SP site up by removing un-necessary controls. It's possible to get very tricky with the look of SP. Below is an example of a site I was involved with that's completely based on SP:
http://www.cableone.net/Pages/default.aspx
Best Answer
In my honest opinion it sounds like you are trying to reinvent the wheel. If users are finding it cumbersome it is generally do to lack of understanding or incorrect implementation and training.
However if you do want to integrate into SharePoint, you can reference the full SharePoint API Library. It is .Net based and allows you to access any aspect of SharePoint in code. You need to reference the Microsoft.SharePoint assembly to access these classes. You will need to setup a development environment for this, since you can't develop for SharePoint without having it installed. The detailed documentation on the namespace starts here
From personal experience we had much more success implement a solid SharePoint structure, with training, and also building the SharePoint portal the same way we would have built a website. Users now insist on having applications in SharePoint.