As far as malfunctions go, do we say that CT is a malfunctioning product because someone figured out you can fight the Black Omen in 1000 A.D....then 600 AD...then 12000 BC? No, it's an oversight on the part of the programmers.
You honestly think that's a mistake in programming? The only question that brings up is not whether the Omen should be around still in prior times, but the paradox created by destroying something in an earlier time period that you fought in a later time period. Hence another reason TTI was brought up in the first place. Rather than approach through the problem on a logical time travelling sense, the programmers simply made it a dungeon you can explore multiple times, prompting us to come up with reasoning for it that is full of contradictions.
i just had to mention that being able to fight in the black omen 3 different times is no mistake, and no paradox. you can destroy it in 1000 ad, then battle it again in 600ad and then in 12000 bc.. because each time, it hadnt been destroyed yet. the fact that it was destroyed in the future doesnt stop it from existing in the past.
if you destroyed the black omen at 12000 bc, then it would disappear in later times.
anyway
the gate key situation is a complex situation. after all, chrono didnt drop the pendant like marle did, right?
we can assume that the dreamstone pendants special properties helped open the gate, along with electric/lightning power from the telepod. theres also the question of the telepod itself and how it worked.. if lucca could create a teleportation device, perhaps she was also smart enough to study the pendant/telepod reaction and craft a device with a similar amplifying effect.
then theres the question of why we couldnt see the gate before it opened, but we can see all other gates before we use them once. perhaps the initial gate opening triggered an entity-assisted chain reaction that made other gates available?
and what if the pendant still had a bit of charge from the mammon machine in 1000 ad, and thats what caused the initial reaction? what if the gate became a stable "closed" gate after chrono went through it, making luccas job easier?
many questions...