1. Acess at home to high school level of chemistry and physics textbooks my mom used when she was in school. Access to interesting SF books, especially short stories antologies as they usually provide best ideas/words ratio. Access to books about DIY and popular, home practical science targeted at children and teenagers. Access to encyclopedias general and topical (some illustrated). Access to 8-bit computer with user manual that taught BASIC. Access to books of logic puzzles. Access to tools and participation in DIY home projects of my granfather that involved wood, thin sheet metal, nails, screws and soldering. Access to things tondismantle and see what makes them tick. Mostly but not exclusively toys. Access to magazines about popular science, DIY, and computer programming addressed at least partially to kids and teenagers. Every monthly issue was an event.

No specific questions or games, and mostly ideas comming from SF and science.

Basically effortless access to colorful, pretty, printed materials about science and DIY and knowledge in general was a key thing for me.

1a. My DIY capable gradfather that let me participate in his DIY projects and repairs. My mother that provided me with all the books and magazines and computer.

2. No idea. Maybe renewables, energy grid balancing, energy storage and transfer and financially beneficial utilizing of excess energy. Maybe how to efficiently house, feed, police and develop and assimilate millions of climate refugees?

Also I was rarely if ever described as gifted or praised even when taking part in school science competitions. I've just seen for myself that other kids are dumber and know less and met kids smarter than me in some aspects only in highschool and possibly later.

So if I have a recomendation for you, ensure variety of engaging materials on science and technology and some SF so she can dream and start doing a bit of easy DIY projects (diy kits) yourself just for fun and let her participate. And keep shush about the gifted label. And be happy for her when she starts figuring stuff faster than you.

Focus more on deserving her love and she'll probably have no trouble keeping herself and her parents afloat before she's 40.

If you want her to change the world, drop that ambition. Being a genius is a baseline for even trying that and luck of being at the right place at the right time and with the right people is the bulk of it.

Also, can't go wrong with LEGOs.

I heard that it's better to praise the work that was put in than some innate cleverness of the child because then when the child encounters a hard problem, she doesn't have identity crisis ("maybe I'm not smart?") and instead just thinks that she needs to put in more effort which is usually more healthy and fruitful conclusion.

Another thing comming from my formative experiences is, you should crush her in some rules based game. Like checkers. This will show her that objective reality exists. When she can see for herself that according to the rules she internalized she lost, and no amount of crying, anger and pleading can change that she'll understand that not everything can be achieved by manipulating people. Some adults never achieve that understanding and can be great in sales and politics but are rarely any good with any technical work where physical reality is the judge.

Then again maybe she can learn that through DIY and my grandma crushing 5 year old me in checkers was cruel and unnecessary. ;-)

I think in general properly developing emotional responses of a child is way more important than any focused nurturing of any gift they might have.