The first version is unclear, although a reader can figure out the intended meaning. The problem is that compatibility and effectiveness are not questions. The sentence promises that it will tell the reader some questions, and then it doesn't deliver.
The second version is better, because after promising at least one example question, it delivers one. However, the question has very strange word order in English. Better would be "how compatible will these developments be with the didactic models?" The meaning of this question is still pretty unclear, though. "These developments" is plural, but its antecedent appears to be "the use of Rapid e-learning", which is singular, so the reader wonders what "these developments" is supposed to refer to.
A problem with both sentences is that it's not clear how "the use of the Rapid e-learning tool" answers any questions, much less leaves some questions open. Based on a look at the article, maybe this is what the authors are trying to say:
Rapid e-learning has proven capable of producing on-line courses more quickly and cheaply than any other approach, but we have no evidence yet about how well students learn from these courses.
Here's a rewording that better answers your question about grammar, though it's less clear:
The evidence from trials of Rapid e-learning leaves some questions open, such as whether the resulting courses are compatible with the didactic models most accredited in the literature, and how effective these courses are.
"Evidence" answers questions, and can also fail to answer questions, so now it's clear what "leaves some questions open". Evidence has to come from somewhere, like "trials" or "observations"; that's now spelled out so the reader doesn't have to guess.
A reader easily understands clauses introduced by "whether" and "how" as questions. "How" is probably more precise than "whether", since compatibility can come in degrees, but wording it with "how" comes out clumsy. Sometimes it's best to sacrifice precision for clarity, especially in this case, where a reader will not be confused.
Instead of "these developments", the new sentence doesn't use a pronoun to refer back to Rapid e-learning. The word "resulting" establishes the connection with Rapid e-learning and introduces the true subject of the questions: the courses produced by Rapid e-learning.
One last, very important improvement in clarity comes from separating the two questions: "effectiveness" is not "with" the didactic models. The word "with" modifies "compatibility" but was conflated with "effectiveness" in the original versions.