Is J4 suppose to be an assassin, a diving light fighter, a Jungernaut or a tank?

Yeah he's pretty generalist but he's restricted by build path. Pretty much anything that has a dash and hard cc is going to be good at whatever.

Yes

He's not a juggernaut - he's got decent burst but if he's building tanky, once it's blown he can't kill you. Juggenauts are slow and high damage, J4 is very fast (2 gap closers) and medium - low or medium - high based on how you build him.

I'm seen assassin J4 work, and he's got pretty good ratios, but in order to kill someone you need to burn your escapes. I guess you could W out...

He's really meant to be a bruiser tank with decent burst, 0 sustained damage, decent CC, and, well, tanky.

Yes

He's a tank with assassin qualities.

All four of his spells have utility tied to them. (Armor Pen, Slow, Attack Speed boost, Terrain change).

Yes