How to focus on the selected object?
Without knowing the specifics of the Maya feature, try pressing . on the your keyboard's numeric keypad. This adjusts your 3D View to focus on the selected object. You can also press / on the numeric keypad to get a "local view" of the selected object (pressing / again will pop you back to the scene view).
To show all non-hidden objects in the 3D View, press Home.
@neckTwi, if you're using a laptop keyboard, there's often a Function key that enables a virtual numpad within the body of your main keyboard. However, you're working on a traditional USB or bluetooth keyboard that doesn't have a numpad, your options are more limited. In that case, your only option (outside of getting a new keyboard) is to remap the zoom and focus feature to another key.
I am on Mac. Ctrl + scroll is doing the thing. Thank you as I found it in key mappings.
What's the opposite of the `Home` function? To rotate the camera without focus on the center?
@DerkJanSpeelman, I'm not sure I fully understand your question. Are you just asking what "might be" an opposite of the Home behavior or are you asking how to specifically do that?
I found that if you press N to access the right side menu, turn on Lock camera to view, then Ctrl+Alt+Numpad 0 to set camera to the current view angle, the press Numpad 0 to view and work in camera view it works better.
Press Home to view full width of the window. Took me a long time and many frustrations to find out.