I then started to suspect that my chat sessions where being monitored and that my hotmail account had been hacked.
I suspect they somehow got access to your system and installed malware/keylogger or a trojan horse. The risk should be minimized by a good virus scan, Do you have one installed on your system?
I had a simple conection consisting of a cable modem hooked up to a basic home router. I use a laptop that accesses the router through WiFi. I also have a desktop hooked by ethernet cable.
Is the network shielded from the internet by a firewall or are the systems all running their own firewall? Is your wireless connection encrypted?
Since that incident I decided to improve my security so I installed SME server 7.5.1. The cable modem is now installed directly to SME server which in turn is hooked uo the home router.
I hope you are running in server-gateway mode, otherwise this does not help you much.
I just want to know if SME Server can protect my network from sniffing programs and what other things can be done to improve network security.
No. As Charlie already said SME Server can not protect you from sniffers. It does however provide a firewall that can already keep a lot off people out, but protection like this is normally done using firewalls, virusscans and unfortunately user discipline. Do not download from unknown sources, scan your downloads before running them. If in doubt do not use it.
I live in Honduras but I suspect that the attack may have come from Colombia. What knowledge must this person have in order to do this?
I doubt you can back that up with arguments and proof, since you seem to lack a lot of knowledge on security and intrusion protection.
Any advice and ideas you might have can be useful to me.
Yup a decent firewall and a good virussscan as already stated.
To make sure your system is clean I suggest you run HitManPro or Malwarebytes Anti-Malware to see if your systems are still infected.