How warm?
it is okay but if you want it to swim around then put warm water in it. but not to warm.
Any dead creature in the water will putrefy and the resultant putrefaction will kill any fish in that water. So yes the dead crab will kill the Betta eventually.
why would you want to kill a betta D:
CLEAN HIS WATER AS SOON AS POSSIBLE!!! Ammonia is produced from the fishes waste. It is toxic and will kill your Betta fast!!! Do regular water changes.
yes
The cover is necessary for Bettas. It keeps the air above the water moist and warm so that when the Betta takes in a gulp of air it will not harm the fish.
Bettas should be kept at around 78F and breed at around 80F. They are like all other fish in that any temperature change MUST be done SLOWLY. A sudden raising or lowering of their water temperature can kill them.
No
yes betta fish have to live alone or one will kill the other.
Yes a light is healthy for a Betta, they need lights for warmth (the light will heat up the water) And Bettas get sick easily so without warm water they will get ill and lose there color and become a gray color.. Which is not pretty.
Not always, but it's very likely. Some females kill males ;)
I'm assuming you have access to a fresh water crab because a Betta will not be able to live in salt water. The crab will attempt to catch and eat the slow moving Betta. It is only a matter of time before the Betta is killed.