Yes, trees can grow there. On the sides and back of the caf?, trees can grow with one space between the caf? and the tree, in the front, it's two spaces between, just like houses.
houses need two empty spaces right in front of them so yes that will work.
i'm pretty sure the cafe also needs two spaces in front of it, on the other sides it just needs one. the cafe has a weird shape w the left side on the front but the game treats it as if it was square so you can't place trees there even though it's not touching any walls.
And speaking of bamboo (5cm/s did ), if you don't mind waiting just to be sure if a bush or tree will grow somewhere, try a bamboo in that spot. Costs nothing if it dies!