Morality is doing what is right regardless of what you're told. Religion is doing what you're told regardless of what is right.
That and God doesn't give a rat's patootie what you do with your pink bits. But I would think she'd be pissed if you made a point to not fully appreciate such a gift.
Asking a question implies there is more than one person in the world, so yes, there are acts that are "immoral".
If you were the last person on the planet, would there be such a thing as immoral? Probably not.
Morality is always about our interactions with others. An immoral act puts our self-interest above others in such a way that does harm. The discussion about types of harm, how much, and where self-interests collide lies the wonderful world of moral philosophy.