For neuter I really think its better to wait 8-10 months instead of 6 like is normally done. It helps with allowing your pup to develop completely (growth plates close), gives him a chance to try to lose those baby teeth on his own. if not, they could be pulled at the same time as the neuter. If there is any concern about your male marking, I can assure you it's a non issue. If you can potty train, you can train them not to mark indoors.
Spay on the other hand... I have no idea. To me who's never had a female dog, it sounds like a timing act.