Am not sure where to go for help/advice/knowledge. I am hoping some people
can give some feedback/advice to my queries.

We used to have a Vigor DrayTek , on a 4MBit line, and a Windows 2000 Server
for web proxy, DHCP & firewall. Everything was fine (web surfing is fine,
MSN is fine, Remote Desktop is fine, etc). Until our Windows 2000 Server
died and we decided to try letting the router Vigor DrayTek to handle all
the DHCP & web proxy.

We started getting lots of MSN dropped connections, dropped Remote Desktop
connections & slow internet. Every now and then we can't access the internet
for a bit (probably due to saturation or bottlenecks).

We got a new router Vigor (next model) hoping it would solve dropped
connection issues. But it hasn't really. We still get dropped connections
from time to time. What is the best/ideal config/setup for a router to
prevent/stop these dropped connections for Remote Desktop & MSN? I mean,
before when we were using Windows 2000 Server, we never got a drop
connection from MSN or Remote Desktop. Now we get it constantly and it's
annoying.

Is there a Network Monitor tool to diagnose what's going on? On the router
should there be a maximum sessions, bandwidth limit, etc?

How many users are we talking about? I've heard that Vigor makes solid devices, but you might be putting too much demand on the poor thing. Sounds like you have two of them now, so maybe have both of them running but each one serving different purposes?

You can use Wireshark to examine what is going on with your traffic. I've never used Vigor, but you should be able to use a web browser or Vigor software to interface with the device and configure the settings you mentioned.

I believe the key word in all of this is Web Proxy. If your web proxy also did caching, then you've likely started sending way more traffic over the wire then your 4MBps connection can support. If things worked well with the web proxy and don't without, I think it's wise that you'd look into setting up a new web proxy instead of upgrading your router.