Those two issues are normal in the gaming laptop world.
My Zephyrus G14 reaches 80°C on both the GPU and CPU, they’re not made to be running at ice-cold temperatures. I got it in late 2021 and it still runs like it’s brand new, even with high temps in AAA games.
Gaming laptop are made to be used while plugged in, on the move. You CAN play games on the battery but it’s perfectly normal that it drains faster than a soda bottle found by a toddler. If you use it on the battery to do light work (database, IDE, YT, Facebook etc.), there are battery modes that will disable the GPU and use the integrated graphics. I get up to 8 hours from light tasking on mine.