1- You probably won't see much difference with surfing, but you would with file transfers on your LAN. The broadband connection's bandwidth is the controlling factor here.
2- The speed of your internet connection at any given time will fluctuate pretty widely. You can get a good feel for its speed by using any of a number of online tools that clock both upload and download speed.
Broadband Reports Tools offer some reliable speed tests that can give you repeatable numbers.
3- Unless you're pinging your site from just outside the server, your ping times probably don't relate to your users' pings at all. It all has to do with the different routes they will get to your site through, and the ping times for each route can be hugely different.
4- Ping time is more related to what's beyond your Internet connection than your connection's speed. In other words, your connection speed controls how fast the data gets to the Internet, but after that, it's all the Internet. Considering that a ping request is typically 32 bytes, that's not much to move, so a dial up connection can get fairly good ping times with crappy speed.
5- Ping time is a function of the bandwidth and speed of the combination of servers, routers, gateways, and other equipment between the user and the destination. It is not at all connected to how a page is coded, but it can be severely impacted by a server with some wierd caching scheme, or a virtualized drive that's not well handled.