You can change the snapping size by clicking the three dots nearby button that enables snapping.
You can change the tile size by changing the "size" value in the cell section.

Though the tiles in the tilemap are placed using the top left position of the tile, if I remember correctly (it is entirely possible I'm wrong). You may need to move your non-tilemap objects so their origin is in the top left corner, or change the snapping size to half of the tile size, to position your nodes.