Your question is too broad for a technical forum; we deal here with specific problems. For general "how to" questions you need to do the research and find the samples and articles that will help to build your project.
I want to develop a DLL that has a web browser embedded in it. ...then load this
DLL into a web browser like IE, Chrome or Firefox.
So you have a web browser (doesn't matter whether you create it or not) and then run it in a web browser.
The question is similar to asking if one would want to run Chrome inside of Firefox.
Don Guy wrote:
Is this possible to do?
It is possible to create a web browser in a dll. To create a functioning browser then one would simply use the dll in the exe and call probably one method.
That said a web browser is a user tool and a client side tool. I doubt there is any need to have a browser that one can embed and moreover it would likely irritate users because a non-trivial number of them are really attached to the browser they use.
Standard browsers can run executable content if the users allow that. The executable content can be anything, so it could certainly start a browser.
But excluding attempts to circumvent security and attempt to hack information from users I can't see any point to this.