| Let say if I was running my own server with my internet speed 1mb and LAN 100mbps, are my clients' download speeds restricted to maximum 1mb of any content from my server?|
If you have a 1 Mbps pipe to the internet, your remote clients share that bandwidth. The rule of networking is you're only as fast as your slowest link. In this case your internet connection is 1 Mbps and your LAN is 100 Mbps. Ergo, external (remote) clients can only download at the rate of the external link.
As ijack pointed out, your actual upload rate is limited by your ISP. On a 1 Mbps internet connection I would expect no more than 512 K and possibly only 128. For a reasonably accurate measure, google "bandwidth speedtest" and run two or three different ones to compare what they say you have.
The other thing to keep in mind is that a remote client will always use as much of the available bandwidth as possible. The more users, the less available bandwidth per user. If you get too many users at one time trying to download, everybody's download will slow down to a complete crawl. It goes without saying this will slow you down as well since it eats up a goodly portion of your available bandwidth.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.