If you use an Energy Search and don't find any Basic Energy, can you then play another Energy Search even though you know it will fail?
Yes, you can search for energy cards even if you know you won't find them. They exist as legal cards, therefore they can be searched for.
Source: PUI Rules Team (2004-01-15), PUI Rules Team (2004-01-22)
If you use an Energy Search and don't find any Basic Energy, do you still discard the Energy Search?
Yes, you would still discard it.
Source: PUI Rules Team (2004-01-15)