Move/Rotate/Scale without needing to hit the gizmo with your mouse I have turned on the Maya settings (I'm coming from Maya, and in the beginning I want to keep the learning curve as small as possible).

Is there (in these settings) something similar like in Maya the Shift+MiddleMouseButton?

Shift+MMB would let you apply the transformations (over one axis) without explicitly selecting the small gizmo. You could just hold your mouse anywhere above the viewport, move globally in the direction of the X, Y or Z axis and it would just transform in that direction.

For me it's a really intuitive way of modeling, because I don't have to select a small gizmo for every transformation.

Is there something similar in these settings?
As @Aardenon said, you can push G to use the grab tool. From there, pushing X Y or Z will lock it to that axis. If you're in edit mode, pushing X Y or Z again will allow you to move your selection on a local axis, and in object mode, this just unlocks the axis.

Also, you can hold Shift + [axis] to exclude that axis from the lock (e.g. holding shift + X will lock the transform to the Y and Z axes).

This also works with the rotate tool (Rkey ) and the scale tool ( S key).