To get the list of folders of a list you can use the Folders property of the SPList object:
private SPFolderCollection GetListFolders(SPList list) {
  return list.Folders; 
  // you can also do:
  // return list.Folders.Cast<SPFolder>().ToList();
  // to return a List<SPFolder> instead of a SPFolderCollection
}
To check if a given user has Contribute permission on a folder you need to get the SPListItem associated with the SPFolder, check for a RoleAssignment of the given user and check its RoleDefinitionBindings for the Contribute Role Definition:
private bool HasContributePermissionOnFolder(SPFolder folder, SPPrincipal user) {
  var contributePermission = folder.ParentWeb.RoleDefinitions["Contribute"];
  var roleAssignementsOfUser = folder.Item.RoleAssignments.Cast<SPRoleAssignment>()
    .Where(ra => ra.Member == user);
  var hasContributePermission = roleAssignementsOfUser
    .Where(ra => ra.RoleDefinitionBindings.Contains(contributePermission)).Count() > 0;
  return hasContributePermission;
}
Usage example
//remember to add using System.Linq; for the above code to work
//SPList list = <your list>;
//SPWeb web = <your web>;
var folders = GetAllFoldersOfList(list);
foreach (SPFolder folder in folders) {
  if (HasContributePermissionOnFolder(folder, spWeb.CurrentUser)) {
  // do stuff
}