Hi Dom - and welcome to the forum.
OK, let me assure you that you are right - your teacher was telling you stereotypes about Americans living abroad, though like every stereotype, there is probably a grain of truth in what she says.
>>American expats generally live in Waterloo ; which is not entirely false but they also live in other areas of our country.<<
Interesting - because I know of no Americans living in Waterloo (not that I know every American living in Belgium

). There are American Women's Clubs in Brussels and Antwerp, so I suspect those cities are both candidates for being centers for American expats. Brussels is obviously a big draw for the Americans, due to the international organizations located there. Antwerp seems to be a big industrial center, so plenty of transferees in that area.
>>The teacher told us her husband has been working with American expats and that those expats buy brand new furniture, including wash machine, dish washer, etc. in the USA before moving overseas where they won't be buying nothing.<<
That may have been the case in years past, when big American companies often provided American-style housing (possibly NATO related), but these days they're fools if they do. American houses are much bigger than what you get in most of Europe, so US furniture often doesn't fit in well. (Though if their employer is paying for their move, they'll often bring their own furniture.) Electrical appliances, however, are very different in Europe - and unless they have the house they are living in rewired for 110V current and make adjustments for the plumbing, they'll have real trouble using those fancy new American appliances. US appliances don't heat their own water, so have to be connected to the hot water system - something that isn't normally done in European homes.
What your teacher may be referring to is the practice of many US expats to sell off their appliances when they leave Belgium to go back home - thus some articles of furniture and major appliances circulate within the US expat community for many years.
The other issue is that I believe NATO has its own PX - a special store on post where people can buy food, clothing and other items from "back home". It's similar to a military base in this sense, and some people live off the PX privileges without buying much in the community. But again, they're kind of foolish to do so.
>>American expats travel to America to see the doctor while Belgium has the most powerful social security system of the world. Is it true? Is it related to the terms of their health insurance?<<
Some people do. It depends on their situation vis a vis the Belgian health care system, and their comfort level with the local languages and customs. I think NATO has its own medical system (again, like a military post). But for other people only temporarily in Belgium, they may not be comfortable going to a doctor who may or may not speak English. (Despite what the guide books say, most doctors don't feel comfortable treating someone in a foreign language.) If they still have coverage back home, they may save up their medical problems for their next trip back to the US - simply to have continuity of care with a familiar doctor.
But those who are staying for the long term are usually only covered by the local (i.e. Belgian) system, and they manage to find the services they need. The US health care system is very different from the Belgian one (and MUCH more expensive), and it can take Americans a few years to fully trust it. I have to assume the same is true of Belgians coming to America.
There are different treatments for the same conditions, different medications prescribed for the same illness and very different procedures for seeing a doctor, being referred to a specialist or being admitted to hospital. Plus, I can attest to the fact that it's very difficult to have to deal with a foreign language when you're sick! So it's not so unusual for people to try to stick with the old system they know for as long as they can.
Anyhow - a long answer for a start. Let's see what anyone else has to say.
Cheers,
Bev