No fix. The charger isn't great, and the phone gets hot. I haven't personally seen it get hot enough to interfere with operation, but that doesn't mean it can't happen.
FWIW - wireless charging is often hot. I prefer to just use a cable.
Yeah, you can push the stock turbo pretty hard. The record for stock turbo/stock motor car is still 9.4 seconds with very little weight reduction + some nitrous. I watched that pass happen at my local drag stip.
Pure800 is what most people on the forums have done. There are a lot of big turbo guys making a lot of power. Going with a big turbo is a huge commitment, and you'll likely spend significantlly more money.
As far a single goes. Single is the only option. Replace the little one with a stock...
HP numbers aren't interesting for the trans, torque numbers are. Stock trans is good to around 550-600 tq, then it'll need to get built.
Curious why you're basing your goals in power and not times though. Do you have a 1/4 mile time in mind you're trying to hit?