Overriding protection
 

I am a new maya user, coming from blender. In blender, if you remove a critical vertex or line, the program allows you to do so and rebuild the faces as you like. However in maya I keep getting messages that "border edges cannot be deleted" and "Warning: Some selected vertices have complex edge attachment; Delete Edge/Vertex removes selected vertices and related edges // ". Is there a way to stop these protective protocols from being activated so I can remove whatever I want without having to remove the connecting faces and edges individually first?

As a side note how do you use the selection box to only select visible faces, lines and vertices without selecting the ones behind them?

Don't know about your first issue, can't really say that I've needed to delete those and come to think of it, I don't know how Maya can define a surface thats missing border edges :x Maybe someone else has a solution.

Your second issue, turn on backface culling, select the object, Display>Polygons>Backface Culling, there are also option for this right beneath that. If you use it enough you might want to assign it to a hotkey or something. If you turn it on in the prefs it'll affect all your poly geometry upon creation (which personally I find annoying as hell).

Thanks for that. Another quick thing, when bridging how do you adjust the number of objects it creates? I keep getting faces with half a dozen lines through them meaining bunches of extra vertices and triangles.

Check the options the 'Divisions' value controls how much geometry will be added, also you can change this even after you do the operation (if you have construction history on) just go to the channel editor and you can find the bridge operation in the objects history.