Hey Mooravioli,
I like your piece. The harmony is weird and complex. I think for this kind of music the danger is making the harmony too unconventional, which makes the piece hard to listen to. A lot of people that experiment, do it too much. You don't: you keep the listener hooked and curious, and know how to tell a story through chords. Another thing that helps is your use of melodic motives. Really nice! I especially like the resolution and ending from bar 195 onwards.
Consider using a tenor saxophone instead of alto, it better suits the melodies you've written. Low notes on sax are often harsh and unpredictable, writing a little higher in the instruments range can give a nicer sound/more freedom to the player to choose the right sound. You can also definitely explore the vibraphone's abilities more. Remember that professionals can play four notes at once! Listen to some bebop vibe players for reference.
Also, five sharps (or four for tenor)? why would you do that to anyone? If you raise everything a semitone (Eb major, concert pitch), your players will thank you.
As for the genre - this isn't jazz. I would probably call it contemporary classical. If you want to write jazz, listen to the music. If you'd like to write in any style, you need to be familiar with that music. Of course that shouldn't discourage you from writing this music at all! It sounds cool, and that is what matters. I just wanted to say, if you call this jazz and show it to a jazz musician, they will look at you like "š that is really ~interesting~ jazz š".
For improvisation, your best bet is to write chord symbols and let one player completely free, like in traditional jazz songs, because that is what players are used to. Saying 'feel free to improvise' and 'improvise less' is very vague, and may not give the effect you want. What you could say is 'feel free to embellish' or something, if that's what you had in mind. In general: if you don't want someone to play the written notes, don't write the notes...