Setting Up Multiple Wireless Points As One Entity?

I work in a medium sized business with 50~ employees. We recently decided to allow wireless access for employees, newer computers with internal wifi, and customers. Now, I'm savvy enough to know how to setup a wireless router without using the instructional CD and just accessing it directly via the IP, that's all fine and dandy. However, the range of one singular wireless router hardly covers 20% of the building.

1: The main network hubs are located in a maintenance room far off in the corner, so setting up a wireless device there was not beneficial. I attempted to set one up via an ethernet port in the middle of the building. This worked without issues, and connected fine, however- The wireless router now has it's own separate set of IPs instead of "being one with the main router/hub." Our default IPs are 192.168.15.***, while this wireless router has created a separate set of IPs with 192.168.1.***. This wouldn't be much of an issue were it not for the fact our server needs to be connected via RDP through some wireless devices. So we cannot type in the typical IP to connect to the server since it's no longer in the same network, this also eliminates printer access. The simple question to all this is if it is possible to have a wireless router connected via a port of the main router still believe it's the same network like hubs do, or does this require a separate wireless device I'm unaware of?

2: The second issue is partially relative to the first. Range. As mentioned, one wireless router is not enough to allow wireless in the entire building. Boosting the signal will still result in weak signals, so the better option would be, at my only knowledge in regards to routers: more wireless routers. So I purchased three wireless routers, however the signal is still spotty. So aside the issues in question #1 to sync all routers together, is there a different device I could purchase or a method to make wireless router's range extended over areas. Like say a wireless router emits a signal, at the weakest point, the signal is boosted in a radius, at the boosted signal's weakest point, it's reboosted with another device, etc. I'm simply unaware as to how this could be done, but figure it exists. As my boss stated: How could airports have multiple access points, they couldn't just purchase these routers over and over and hook them up everywhere like this.