"I am a young, passionate, just graduated from university developer. Looking for a dream team where I could get challenging tasks, interesting experience, new friends and an environment where I can grow not only professionally but as well as mentally" is this sentence grammatically correct?
This is correct usage of "as well as", but some parts of the sentence are a bit awkward.
You are using "just graduated from university" as an adjective, so it would need to be "just-graduated-from-university". Either way, it's awkward. Consider "I am a young, passionate developer who just graduated from university." In American English, it would be better to use "college" instead of "university".
It would be better to start the second sentence with "I am" just like the first.
The verb "get" is being used with "interesting experience", "new friends" which is a bit awkward. It is more correct to say you "have" interesting experiences and "meet" new friends.
Non-grammar advice: I'm a manager and speak to groups about careers, resumes and interviews. Here is a bit of advice I always mention in my talks: Concentrate on what you can do for the company, no what they can do for you. A manager is looking to fill a need, not to help someone achieve their dream. Of course, a good manager knows that hiring someone who would enjoy the job gets them a better employee. But the primary goal of the company is to fill a specific need and the manager is looking for who does that best.
Also, probably everyone that applies for the job would say the second sentence describes them. Try to differentiate yourself from other job-seekers. What do you have that they don't?