Also, is there a way to keep the login page in a SP application?
If not, make a common applicataion be the idp? Even if I call resources that are not protecetd in Idp after an sp has redirected to the Idp, I can't make it work. Am I doing something wrong or the Idp application cannot have some basic functionalities to be accessed before the user is logged on? (Like recovering the password by e-mail if a user forgot his password).
In PL 2.0.3, we have added some fallback mechanisms at the SP side. Take a look at release notes.
The exception you are seeing is when your SP is doing redirect and the IDP is sending back POST and vice-versa.