When traveling with airplanes internationally, do they scan/check the non-hand baggage which is separated from the people area in the plane?

Do they scan and check hold baggage? Absolutely certainly they do. Ever since the Lockerbie bombing in 1988 hold baggage has been routinely scanned and checked. It will probably be checked before you board the flight by security, and may be checked at your destination by customs. That applies to both outward and return flights.

There are many things, mostly items that could be used as weapons, which are banned in cabin baggage but permitted in hold baggage, for exactly the reasons you state. Sometimes the item has to be declared to be allowed. Check with your airline about whether the item you want to take is permitted. If something is illegal to carry in your country then there are probably restrictions on how it has to be transported. If you don't follow those restrictions you do indeed risk arrest and imprisonment. If the item is illegal to possess then the risk is significant, and no transportation protocol will save you from it. If the item is illegal to carry in your destination then it is probably illegal to import without special permission, and you risk confiscation and arrest at your destination. Check with customs for your destination.

You might want to rethink your personal protection plan. Despite some perceptions, there are virtually no places in Europe or the USA where carrying an illegal weapon is going to improve your actual safety (rather than just making you feel safe). Unless of course you are engaged in dangerous or illegal activities.

Hold luggage will most definitely be scanned before being loaded onto the plane in most civilised countries nowadays (checking for bombs and other such devices).

In most places this is done behind the scenes after you drop your luggage at the counter. If they find anything suspicious you will get paged and won't be allowed to board until and unless they are satisfied. A long time ago I once carried a paintball gun from Europe to the US and back and that took quite a bit of explaining each time when they detected that thing which looks a lot like a real gun during scans.

In a few places (quite frequently in the US, but it also happened to me somewhere in Greece at least) this is actually done in front of you: when you check-in, they tag your bag, but give it back to you instead of sending it directly into the system. You then bring it to the scanner yourself, and you stay there until they give you the all clear.

In many places, customs also scan at least some of the luggage behind the scenes before it gets on the belt at the destination. If they notice anything suspect they will alert staff who will "randomly" select you for additional questioning and searches.

In some places scans are done more openly, either for nearly all passengers (mostly for quarantine enforcement, e.g. in Australia) or random passengers. In any case, if customs select you for inspection, they will open your bags and/or scan them.

Customs usually work in coordination with the immigration officers who will flag anyone in any way suspicious during passport/visa control for further inspection.

If it is illegal either at the origin or destination, just don't carry it. Fines can be steep, and in some situations there can also be prison sentences. Not to mention the possibility you could be frog-marched to detention and onto the next flight back home with a big black mark on your record.