Carte de sejour

Yes you need to register at the local maison communale / gemeentehuis as you will be here for more than 3 months. You need proof of where you'll stay and what income you will have, plus you national ID / passport. You can  opt for a residence card but it's not obligatory, the alternative is that the paper form of your registration + national ID/passport must be carried at all times. In French it's known as "attestation d'enregistrement" not carte de séjour.

Ok...So its obligatory. Does it take long? And also shoud i have to pay taxes maybe afterwards?? Thank you!

How long it takes depends on where you choose to live. If you want a long wait, then live in Bruxelles Ville, St Gilles, Schaerbeek. If you want a short wait, live in Watermael-Boitsfort, Woluwe-St-Pierre or Woluwe-St-Lambert.

Yes everyone who lives in Belgium for more than 3 months is subject to filing for income taxes. Perhaps there is an exemption for a stagiare, but you'd have to check that with your employer.

For six months, don't even bother. The process will take so long that ypu will not hear from them until you are already gone. Of course, you need to live  like a tourist, no bills on your name, use your national health system, I have heard stories of people who go on like that for years .... due to tax and other reasons.

Yes i hear its a really lonng procedure and i dont feel like getting myself into that.. i dont have anything in my name but i already opened a bank account

and also my house contract...

You don't need a bank account, unless you want a credit or arrange a bank blocked account for the flat, unlikely for short term rentals. If you have a bank anywhere in the euro zone, then you can use the cards and bank transfer services of your bank back home. Now that you have an account, bear in mind that some banks will ask prove that you are registered in Belgium.

No they didnt ask me any proof of registration.. Just a proff of the stage..

It took me 2 weeks to register.....

If you don't register and are asked by Police / Tax / any Belgian official, then you can be fined.

The choice is up to you.