If I cast the giant, not paying the kicker, and then with the ability to destroy all my creatures on the stack, activate Zedruu's donate ability and give it to another player what happens? do I lose my creatures or the player who inherited the giant and why does it work that way?
You will lose your own creatures.
Desolation Giant enters the battlefield under your control. When the ability triggers and goes onto the stack, you control the source of the ability, and as a result you control the triggered ability itself. Once the ability is on the stack, anything that affects its source doesn't affect the ability itself. This usually applies to the case where removing the source of an ability doesn't stop the ability from resolving, but it also means that if the controller of the ability's source changes in the meantime, this doesn't change who controls the ability on the stack.
If I cast the giant, not paying the kicker, and then with the ability to destroy all my creatures on the stack, activate Zedruu's donate ability and give it to another player what happens? do I lose my creatures or the player who inherited the giant and why does it work that way?
You lose your creatures.
The ability on the stack is not tied to its source (the Giant) like that. Giving control of the Giant to another player has no effect on the ability. You still control the ability, so when it resolves you will still be the "you" on its text so you're the one to sacrifice your creatures.
Giving your opponent control of Desolation Giant won't have any effect on the ETB Trigger. It will still destroy all other creatures you control. The reason is that once the ability is put on the stack, it exists independently of the source that created it. Donating the Desolation Giant is changing the controller of the source, but doesn't affect the ability at all.
Since you were the one who put the trigger on the stack, you are the controller of the trigger, and thus you are the person who is referred to by the "creatures you control" part of the ability.
Desolation Giant
If I cast the giant, not paying the kicker, and then with the ability to destroy all my creatures on the stack, activate Zedruu's donate ability and give it to another player what happens? do I lose my creatures or the player who inherited the giant and why does it work that way?
Desolation Giant enters the battlefield under your control. When the ability triggers and goes onto the stack, you control the source of the ability, and as a result you control the triggered ability itself. Once the ability is on the stack, anything that affects its source doesn't affect the ability itself. This usually applies to the case where removing the source of an ability doesn't stop the ability from resolving, but it also means that if the controller of the ability's source changes in the meantime, this doesn't change who controls the ability on the stack.
You lose your creatures.
The ability on the stack is not tied to its source (the Giant) like that. Giving control of the Giant to another player has no effect on the ability. You still control the ability, so when it resolves you will still be the "you" on its text so you're the one to sacrifice your creatures.
Since you were the one who put the trigger on the stack, you are the controller of the trigger, and thus you are the person who is referred to by the "creatures you control" part of the ability.