In the Moreh Nevuchim, Rambam explains how God's attributes should be understood without compromising God's unchangingness.
He compares God's mood to a fire. If you put ice in a fire, it melts, then evaporates. If you put clay in a fire, it hardens. If you put wood in a fire it burns... The fire causes many different and contrasting effects without changing the fire's properties. The same "fire melts certain things and makes others hard, it boils and burns, it bleaches and blackens." It is the properties of each individual material that elicit a different interactions with fire.
Similarly, our actions change properties within ourselves, and it's those changes that elicit different interactions from God, without God changing.
Additionally, Rambam explains that God's "jealousy and wrath, kindle His fire and anger" are reactions solely elicited by idolatry. By worshiping idols, one makes them-self an enemy and adversary of God.
I don't think "happy" is a word we can use to describe God, it's a human/time-related state of mind. If you follow God's commandments though, He will turn His face to you - meaning Hashem will pay specific attention to you, and watch out for you.