Buying property isn't easy. I hope I can help you with some of your points.
1) What do you think about the requalification of the Goethequartier and in general about the perspectives of Offenbach? Will it be successful?
Let's start with... well... the reputation. You shouldn't rely too much on local opinions.
Within Hessen Offenbach has quite a bad reputation but that's more about an ever ongoing rivalry between Offenbach an Frankfurt.
Frankfurt has quite a bad reputation in Germany as Offenbach has one within Hessen. I personally think neither city is deserving it.
Now about the area you're interested in. Nordend (which Bettinastraße is part of) is currently benifiting from the ongoing developement at Offenbach Quays (Hafen).
Also transport-wise the area is fairly attractive. Frankfurt City Centre can be reched in just 10 minutes from Ledermuseum or Kaiserlei Station while trains run every 5-10 minutes. There also is a 24 hours Metro and Bus service between Frankfurt and Offenbach leaving Offenbach better connected than some parts of Frankfurt.
Two Main-Line Stations (Frankfurt Hbf and Hanau) are accessible in approx. 15 minutes from Offenbach City Centre.
There are also Cinemas (Cinemaxx, unfortunately less interesting if you're don't understand German as they lack OV screenings and Hafenkino) nice restaurants and the Capitol Theatre in walking distance.
At last, will Offenbach be successfull? Frankfurt and Offenbach form the core of the whole Region.
As Frankfurt runs out of room and Offenbach being closer to Frankfurt City Centre than many of Frankfurts own districts I think Offenbach will be in a very good position.
2) Do you think the noise originated by the plane is a serious issue for the value of the apartment?
I don't think so. Especially new buildings are well sound proofed. Noise shouldn't be too much of an issue. Also you can't really avoid noise polution anywhere in Rhine-Main. Most parts of Frankfurt have the same problem.
3) Which aspects, in your view, should I consider before to decide to buy?
It depends. If Frankfurt is out of your budget but you would like to live in a city. Offenbach is probably a good option.