I am in a process of preparation for applying for a MEXT scholarship
As I recall, MEXT accepts any level of Japanese and if your level is low they arrange Japanese classes for the first half a year? year? of your scholarship period before you take the entrance exam to officially enter the university program.
what the recommended Level of Japanese In order to be able to safely communicate with the professor and research colleagues
To be brutally honest, at least N2, preferably N1. All the international students in graduate programs I know here had this highest level. The following mixes my experience with information from the Summary of Linguistic Competence Required for Each Level of the exam:
N2 is about using Japanese in "everyday situations", so daily conversations would be no problem. And N2 is when your technical reading starts to get good. Understanding "lectures spoken at natural speed" is N1 level but you might get by with N2. Technical communication one-on-one or in small groups might also be OK -- the other participants can mix in some English and also accommodate your level of Japanese in other ways (speed of speech, vocabulary choice, etc.).
But a lot of academic life involves technical discussion among many people -- seminars, workshops, research/study groups, etc. -- where accommodation of the one foreigner is more difficult. Surrounded by many Japanese debating technical matters at native speed, I feel you need to have nailed the highest level N1 to keep up.
Is English pretty much favoured in Japanese Universities?
Some universities have some specific programs conducted in English. But besides that, in my experience, no. In my field* (and probably yours) at least a lot of the reading and writing of papers can be done in English. But Japanese students and faculty are the great majority, they speak in Japanese among themselves, and classes are conducted in Japanese.
Seminars, study groups, etc. (among students and faculty), as well as symposia, conference presentations, etc. (national organizations) tend to be in Japanese. High level Japanese seems to be necessary to get the most out of academic life here.
* I was in an English Linguistics dept. and communication was conducted primarily in Japanese. Your more technical field might be more 'international' (though some stories I've heard and a quick look at some conference programmes don't make me think so).