You use a net.
no
winter
No, you cannot catch a shrimp on Animal Crossing (for the Nintendo Gamecube), nor can you catch a shrimp for any of it's successors, Animal Crossing: Wild World and Animal Crossing: City Folk.
You can catch a coelacanth when it is raining or snowing
in december.
Catch all bugs.
you catch them in the ocean in June onwards
no you can't
your house can't catch fire.
There is no such bug as a rain stag.
Down by the sea at random times
i think you have to catch every bug