Nothing weird about being more active as the temp rises, they are more active at optimum temps.
Hard to tell the species from the photos... a checkered? Or radix?

Shed period... Don't worry about 2 months, our albino checkered shed last night for the first time in 104 days, the gap between their previous two sheds was just 23 days. She's about 9 months old as well. So that illustrates the variation in shed intervals.

The spot on the belly - does it have any texture? Is it raised? I'm not seeing anything that would concern me there, but like many things, it's something I'd keep an eye on.
The vent looks like something I'd ask questions about. Is there anything discharging from the vent? It looks like there's some yellowy stuff there? Does she musk a lot? Does she poo regularly after eating?