I can only tell you about my experiences...
1) How long? It depends. Apartment rental have been around in Europe for a long time. It used to be mostly for a week from Saturday to Saturday, but mostly anything goes now.
2) Buyer beware - It will be up to you to research the neighbourhood. You can do that many ways. Perhaps the easiest is using google streetmaps
3) There is no one way to check in. Sometimes you meet the owner or manager and they will give you the key. Sometimes there is a combination lock on the door that houses a box where your keys are, and the owner just gives you the combination.
4) There are too many good sites to mention. Airbnb, VRBO, homelidays, etc etc. One good way to feel good about the place your staying in is to cross reference it with another site. My experience is that most rental properties appear on more than one site. Cross reference and read the reviews.
I've rented many apartments over the years, and only once was I really disappointed...but there is much more due diligence for you to do than if you get a hotel.