How to control fields displayed when selecting a Lead or Opportunity to associate with a Custom Obje

I am using custom object 3 for a purpose that requires users to associate it with one or more existing opportunities, and also one or more existing leads.

On the Custom Object 3 layout, I have exposed Leads and Opportunities, and the New and Add buttons are both active.

(a) Can I enforce having the Add button active but not the New button?

(b) When I click Add, the Search for a (Lead) or Search for an (Opportunity) window comes up, and lists all the choices.  However, the fields that are displayed are not sufficient to quickly identify which Lead or Opportunity I need.   I want to display specific other Lead and Opportunity fields in this window to help more quickly narrow the choices.