1, if your model does not have edges aligned to the middle axis then what you do is... (this may look long and seem like a lot of work, but you do it enough times to do this in a few seconds and skip some of the steps because it's already been done in some cases, alternatively, write a script to do it and you'll do it in less than a sec)
make sure your edges you want merged are aligned...

• switch to vertex selection mode
• grab the vertices you want aligned to the axis
• hit w (the move tool)
• hold w down, left click, and make sure world is selected, not object. if object is selected then the verts will keep their spacing between each other and will not align to an axis
• hold x, and move along the axis you want to align to
• this will snap all the verts to that axis you want to snap to.
• move the verts to wherrever you need them

then align the model to an axis at the origin (0,0,0)

• hit insert (if on windows) hit home (if on a non macbook), if you're on a macbook then i have no idea what the button is because apple is stingy with their keys
• this will allow you to change the pivot point. grab the pivot point
• hit w to select the move tool
• hold down v and move it along an axis. it will snap to align to verts
• align it to the verts that are aligned with each other
• hit insert to get out of pivot point mode
• now hold x and move the model to align to an axis thats at the origin

mirror the mesh and then select the two meshes. Mesh > Combine them and then select the border edges of both meshes and click Edit Mesh > Merge

the key thing is, you can change the pivot point and snap it to align with vertices. models snap their pivot point to whatever your trying to snap to. i'm sure you can figure out how that's useful and how to use that

2, do the tutorials that come with maya, you'll figure it out there. one of the first ones (the one that does a helmet i think) tells you what you are wanting to know
but the 1,2, and 3 keys are the 'smooth preview' keys. the 'artefacts' you saw was probably the original model in the same place as the proxy.

3, dunno about the manipulators. maybe a graphics card glitch. anything graphically flawed is a graphics card glitch (i just saw a thread that you might want to look at, it's named Maya 2010 (yeah, bad name for a thread) and someone is asking the same question as you)

4, undo and redo in maya is very detailed. if you select something and hit undo it'll unselect it. from maya 2009 upwards they did something clever that's been done in some other graphics programs for ages.. highlighting what you're going to select before you select it. of course, if you're not on 2009 or up you'll just have to hit undo whenever you click something accidentally.

5, huh? it looks like you might be trying to delete a border edge there? which obviously cant be done.
but if it's not a border edge then it does what it's suppose to. deletes the edge.
if you have a cube and delete an edge you get a face that has 6 edges. if you dont want that face then delete it... sometimes n-gons are useful (ctbram will tell you that!)