1. Is this figure real?
Yes, it is! Though you need to be careful about fakes, where people just paint any Magikarp Tomy in a gold color.
An auction popped recently that had the Magikarp still sealed in package.
2. How much does it cost?
As of October 2017, a packaged gold Magikarp fetches 125,000 yen and this is roughly 1,100 USD. In the past, not mint condition/opened ones have gone for around 50,000 yen and this is roughly $440 USD.
3. Where does it come from? What lottery gave away the Magikarp?
This was the most fun part of my research. The gold Magikarp was given away in 2005 during the Pokemon Daisuki Club's "Summer Vacation Biggest War! 2005" event. Source (Google translate might have butchered the actual contest name)
The way you won was by playing a fishing mini-game on the official Pokemon site in Japan. The first 2,000 people to fish up a gold Magikarp, would be given a Tomy figure. The Internet Archive Wayback Machine still has the page available for viewing. The mini-game page is now broken and you can no longer play the games but it's still interesting to be able to see something so old.
4. How many figures were made?
2,000 of them.
5. What keywords can I use in Japanese to search for the figure in auctions or shopping sites?
There's a couple. The one I mainly used for research was モンコレ コイキング 金色 (Moncolle Gold Magikarp) but you should be able to find one by just searching コイキング 金色 (gold Magikarp). To narrow down your results since Magikarp also has a golden plush, can just put the word Tomy along with the other words I've mentioned. The one the seller used for the most recent auction was プレゼント モンコレ コイキング 金色 (present Moncolle gold Magikarp). Present as in the fact that it was won.
I think I've covered all bases for this figure but if anyone has any other questions, you can comment below even without an LJ account and I can try to dig up stuff for you.