1). Split Polygon tool has a snapping tolerance option, you can choose how powerful to make the snap, and where along the line to snap. It defaults to 50% along an edge, if you increase the tolerance then it will be more likely to jump to exactly 50% if you're near the middle of the edge. Unfortunately without custom scripts there is no other way to do this. To triangulate the edges the fastest way is probably just to stay in the Split Polygon tool and hook up the verts manually. Either that or select each face and do Mesh -> Triangulate.
It seems like most old-school Maya users do a lot of their work with Split Polygon tool, which frankly I find quite scary since it's much slower than many other (more modern) methods... although it is obviously a very useful modelling tool, I don't think it should be used for quite as much as you're forced to use it for.
2). Spacebar by default, tapping it will toggle whatever viewport display modes you're in between fullscreen or not. If you were in a 4-view display by default, just tapping spacebar once, mousing over a different viewport and hitting it again will put you in that view, fullscreen.
Alternatively, a faster way can be to hold down Space to get the hotbox up, click and drag in the middle, it should give you all available camera views in a radial menu. Pretty fast.
3). Yes, another thing which is painful to behold. There's no preview or interactive setup BEFORE you bevel (although I believe Funky Bunnies made a script which allows this). The best way to do it is just to bevel with default options, then go into the History list in the Channel box, expand your polyBevel node, find the "Offset" value, highlight it, and middle-click drag in the viewport to change the value.
Middle-click is like the "magic button" in Maya, it's what the majority of interaction can be done with, and is often very fast (for example you can drag-select over a Rotate field in the Channel box, then middle-click in the viewport and it will rotate only around that local axis).
4) Unfortunately, yes. There's nothing as straightforward as Max's "Symmetry" modifier. The closest you'll get is by assigning a "Mirror Cut" node to the Output list of your mesh, but that's not exactly a friendly workflow (by default it gets placed in the Input list).
Please note that all of these answers are "to the best of my knowledge". Do not take them as the final word, it's entirely possible that someone else has better solutions... although I have been using Maya for at least a year and a half now, so I'd hope that if there are better solutions, then they're not immediately obvious ones, or I'll be kicking myself