Shutdown the CHR and increase the HD size in ESXi allocated to the CHR. Restart the CHR and it should automatically pick up the increased disk size. You could also add another virtual drive in ESXi for the Dude files. This will stop it over running and crashing the router when it runs out of space.
Yes.
You should allocate at least 2GB if you plan to run the Dude as a trial. If you have a more extensive requirement for the Dude you need to plan ahead.
I remember, and I might be wrong, that they have limited the boot drive to 1 GB. I have not tested but think I remember reading this a changelog.
So as stated before add another drive as well.