so just a disclaimer I am no expert, however, my first thought when I saw the first picture was that it was a copepod. More specifically a Harpacticoida (I had to google the spelling for that).
I don't really know a whole lot about copepods, what I do know is that copepods aren't harmful to your aquarium, in fact, it's a good sign that you have a healthy ecosystem in your aquarium. So there's nothing to worry about, I know some fish will eat them, but theres nothing to worry about with that either, its perfectly natural.
As for the second bug in your tank I have to admit I can't commit an answer with even 50% certainty. Though my best guess would be that it is an ostracod, or more commonly known as seed shrimp.
Though I have very little knowledge on these. There is debate on the matter of whether or not these are beneficial as some people report that they can kill fish if they have nothing to eat in the tank. Though these are all guesses on what caused the fishes death, without any proof (at least the accounts I've come across anyway), so it's better to wait for someone who has better knowledge on these critters than I. If you could get a better picture of bug #2 that would probably help, the video was a little shaky (but I understand, I can't even record my cat let alone a bug on a pane of glass).