[MauranKilom]

> Do chess engines strategically use up their time depending on the complexity or the criticality of the position?

Yes, this has been something engines have started to optimize. Some engines that don't do this well can be beaten by "flagging" (i.e. making pointless moves rapidly) once they run low on time.

> Do both chess engines have equal machine power, cores, IOPS, CPU model, RAM, etc?

Last I remember, the goal was to give engines roughly equal computational capacity. But it would be tailored to the engine, e.g. AlphaZero getting something with more GPU(s) and StockFish getting (at the time) more CPU(s) - at least for the final matches.

> They're showing a game with an eval bar

For me, it shows the current evaluation of both engines (numerically), as well as a graph with up to four engine evaluations (the two contestants + up to two "commentators").