How can we add a new action (like Edit & Delete) for each record on the standard list page (Salesforce Classic)?
No, it's not possible. What you can is:-
Customize the buttons on the list view i.e in your case, you can add a button near the new program button.
Add or remove Custom buttons In Aloha
For standard objects
i. From Setup, click Customize | then click the object you want to modify | click Search Layouts.
For custom objects
i. From Setup, click Create | then click Objects.
ii. Click one of the custom objects in the list.
iii. Scroll down to the "Search Layouts" section.
Click Edit next to the List View layout
- Highlight the values and click on the Add or Remove button to toggle the visibility of the button on the layout.
- Click Save.