I simply ask myself rather one could make sense of the Dharma and apply it without the concepts of rebirth and kamma? 

Though for me it is my personal approach to the Dharma, which i find to be highly meaningful in both theoretical and practical manner. As like no other intellectual complex, I think the Dharma could claim something like describing the essence and nature of being - if such claim should ever be stressed.
I would not dare to discuss this question as a devout follower. My interest is simply philosophical in its nature.

So i am just about to read C.W.Gorwans "Philosophy of the Buddha" and I am very pleased about how well balanced and respectful he treats the topic as a scholar of analytic philosophy. 
Considering the concepts of kamma and rebirth, ONE of the approaches the author offers, is that the Lord Buddha just simply took kamma and rebirth as beliefs deriving from his culture, beliefs so deep and taken for granted that he would not spend a second on doubting it - although he must have been very critical to all kinds of believe. But for example, if you consider doubtful questioning in western philosophy, such as "the meditations" of Descartes and Husserl, it seems mostly obvious that doubt could never ever stressed out in the whole sense. Even though while claiming that radical doubt will set up everything to the disposition of rational examination, there will always be some "leftover" belief as remains (for Descartes it was god , for Husserl it must have been the ego). The latter should also be a position that C.Taylor stresses in his historical treatise "Sources of the Self". 

Ok, but coming back in addressing my question to you as experts in the Dharma, what are your opinions about this issue? Could we make sense of the teaching of the Lord Buddha without believing that we will be reborn? 

As for the concept of kamma, it is possible to make sense of it without believing in rebirth.

Well I do not expect a discussion on a very high intellectual level, but maybe an exchange of ideas and opinions on the applicability of "Buddhism" and its precious teaching in a mindset that could be called "western". 
As I found out that it is a major critique of native Buddhists about western fellows that they don't sufficiently reflect the teaching according to their own culture and should not simply adopt it as a belief - which would actually be contradicting the Dharma.

warm regards!