Hey there, I do lot of ELISAs for HIV antigen/antibody detection.
First, in regards to your goal, 96 well plates are limited to a minimum of 25ul for the reaction because of the surface area of the well in a 96 well plate. 384 well plates (what we use) bring this down to as low as 5ul and the increased amount of wells also ups the throughput. Since ELISA are extremely sensitive, once you add in the dilution factor and your actually limited by the fact that you don't really want to pull less than 0.5 ul from a sample w/ a standard pipette. Washing/blocking is also dependent on the type of assay you’re trying to perform and your available detection reagents.
Here are the answers to your questions.
A few problems you might run into
I think your best bet is to contact a lab that does ELISA’s in your area and see if you can get little funding from your school to cover the cost in materials to run an ELISA there. Or alternatively you can prep your samples and send them off and it will probably be around $100 per plate.
Good luck!