- The official rule is that you can not interrupt your journey with a regular ticket. To do this you need a "Via" ticket. Source (click on "Can I break my journey?")
- You can take either the shortest or the fastest way or a longer way that allows you to do it with less changes of train. If you find the journey in the planner on their website, it is certainly fine. As long as you are traveling towards your destination you will be fine. They are not too strict about this. If your journey involves a stop in Brussels (Midi, Central, North...), you are officially not allowed to interrupt your journey there, but it is very hard to verify so you will get away with it.
Now, for your specific journey all options in the planner on the website involve a change in Antwerp, not in Brussels. So you will not get away with visiting Brussels. An alternative would be visiting Antwerp. You will get away with that, even if it is strictly speaking not allow to interrupt your journey there.
A ticket to Brussels-Midi would be one to "Zone Brussels", which includes all stations in Brussels. The airport is not in this zone, because the airport is not located in Brussels proper, but just outside of it.
Finally, you will not find anywhere on the website of the SNCB the ticket described as a ticket to Brussels plus surcharge. You will find it described as a ticket to Brussels Airport-Zaventem, as the airport station is called (formerly Brussel-Nationaal-Luchthaven) including the surcharge.