Silver Stripe, like any other CMS, is not really a program but a website. You unpack it into LAMP's htdocs / public_html folder and visit the index page to set up and edit the web site.

(Just go to http://localhost on the Pi)

When you register a domain, you can make it point to your raspberry Pi by

a) getting a fixed IP address from your internet service provider or using a service like noip.com

b) setting your router's port forwarding to forward port 80 requests to the raspberry Pi.

For a project I am making a web host server from a raspberry pi, installing LAMP, etc

1.I plan to use Silver Stripe as my CMS. Do I need to be running the program on the server itself or can I "make it" on my laptop and somehow put it on my server?

2. I plan on buying a domain name as well, how would I connect that to my website that is hopefully by then located on my server?

These are probably stupid questions but I am new at this. Thank you for your time.