Where does evil come from?
Not from G-d, evil is the absence of G-d. G-d is the source of love, pure, infinite, etc. When G-d is not in that space than that space (or person) becomes... impure, finite, love-less.. less than what is needed to be called good.
Why does good have to have an opposite?
I'd think because that's the nature of the situation. Good is perfection... less than perfection is evil. Functionally, the opposite of good is there because of the situation. To go off into a slightly different direction... "Why is there a difference between good and evil?" Because there's a moral standard. Why does good have to have an opposite because the moral standard make it so there's a differentiation between good and evil.
God is all good. Did He WANT us to experience evil?
Maybe, yes, he did so that can see the difference... maybe so that the experience/struggle between good and evil would move us towards him... I can only guess. No, he didn't because that was never his purpose... however, because we humans have chosen evil/sinned then we have infected ourselves and the world for evil to be around.
Did He create it for this express purpose?
I'm not sure what you mean by this question.
Why did He give us choice?
Morality requires intentionality... free will gives us intentionality. So, if G-d wanted human beings that truly were capable of goodness than free will was necessary so that goodness would be possible.
You're saying it's our CHOICE that creates evil?
Choice doesn't "create" evil, choice... bad choices specifically can be the a way evil could happen though.
Or that it exists so that we may have choice?
I don't think its necessary for evil to "exist" first in order to have choice. That's like saying... Here's a smartphone... and here's an old cell phone... the old cell phone has to exist so your capable of choice. Actually, I think you could very well have freewill without the old cell phone. You could have an abstract understanding that the smartphone is good and the old cell phone is evil. Freewill or having a choice isn't dependent on "evil" existing. However, it may be dependent on G-d giving us the abstract understanding between right and wrong.
What kind of a God would that be?
A G-d that truly wants goodness to be possible in our lives. Without freewill... there's in intentionality... without intentionality... there's no goodness... no love, no kindness, no charity, no anything right.
Do you have a pet? Do you throw him out into the rain so he could have a choice to come back into your warm home?
Nope, but the pet does have a choice to go out into the rain. The pet could possibly dig a hole under the fence (my dogs have done this -_-) and run away... be on your own... possibly starve or die due to the dangers of being a domesticated pet in a human world... reminds me of sin.
Remember... G-d didn't throw us in the rain... he threw us in a beautiful paradise garden where there was no need for labor and mankind walked with G-d. We sadly chose to dig a hole in the ground to get past a "loving" fence and now we face a world... with sin where we must ask G-d for forgiveness and go back home.