If I have LAYER A and LAYER B, and LAYER B consists of a large object---  When I select LAYER A, and paste a smaller object into it and proceed to click and drag on that pasted object, instead of the object moving, the large object on LAYER B moves.

This behavior has caused a lot of frustration, and I am assuming there must be some way to lock the current layer I am working on so that it auto selecting objects on other layers..  Is there a way to prevent this form happening?

Also, what is the key command for zooming?  Most programs have cmd +/- keys for zooming, but this is not the case in Inkscape.  When I look at the menu bar under View > Zoom, there are no key commands listed so I have no way to know what they are?  Are there not key commands for zooming?

I feel your pain; go to Object->Objects... and lock the object you don´t want to select&move by accident.

Zoom is usually just +, -.

Layers can be locked using the Layers dialog. Objects and layers can be individually locked in the Objects dialog.