Can I just paste compied folders onto a new computer?

I am now sharing a computer with someone (we each have our own User Account). I copied all of my folders/documents that were under the Program Files folder on my previous computer onto an external drive.

Can I now just copy those folders and paste them under the Program Files folder on the new computer I'm now sharing?

No they need to be installed. That is the only way to update the registry with all the needed infromation for each program.