Can you browse websites from Mars? The answer is "theoretically possible but practically impractical." Earth-Mars distance ranges from 55 million km at closest to 400 million km at farthest. Even at light speed, one-way communication takes 3 to 22 minutes. Clicking a link from Mars means waiting 6 to 44 minutes minimum for a page to load.
This delay is fatal for current internet protocols. TCP requires multiple round-trip communications for a single page: DNS resolution, TCP connection, TLS handshake, HTTP request/response. On Earth, these complete in milliseconds. With Mars, each round-trip takes 6-44 minutes, potentially requiring hours for a simple webpage.
NASA developed Delay-Tolerant Networking (DTN) to address this. DTN bundles data and stores it at relay nodes, designed for communication delays and interruptions. In 2008, NASA successfully tested DTN between the ISS and ground. Space books are available on Amazon.
If humans settle Mars, a "Mars internet" would be needed. Real-time Earth website browsing being impractical, local Mars servers would cache Earth websites with periodic syncing, similar to early internet "mirror sites." Mars users would browse Earth websites that are hours old.
Short URLs could play an important role on Mars internet. With extremely limited Earth-Mars bandwidth, data reduction is paramount. Converting long URLs to short ones reduces communication data. Mars-local short URL services would need to operate independently from Earth services. Perhaps a "mars.link" domain will emerge someday. When humanity ventures into space, the concept of URLs will travel along.