1. How do I install texture packs onto my server?
You should be able to just upload the texture pack to the root of your servers FTP and then under the "texture-pack=" line your server.properties add the name of it and restart the server.
2. How do I install mods onto the server?
For the most part you just need to upload them to the plugins folder in your FTP after installing Bukkit. However, each plugin/mod has its own instructions that should be provided when downloading it.
3. I am getting some lag on my 5 man server, if I upgrade to say a 10 man or higher, does performance improve on the server? My server is pretty massive, I have probably placed over a million blocks easily, but I am not sure if this effects server performance.
Lag can be related to a lot of things, on smaller servers like yours it can be something as simple as blowing up to much TNT or some insane redstone circuits, on bigger ones it can be related to plugins or other mods.
Since you are asking how to install plugins, is it safe to assume you are running a vanilla server?