click on the object (selected), go to editing menu (F9) and press center new. or put the 3d cursor somewhere and press center cursor. the center options are under the mesh tab
You know about ctrl+r option? it's cutting, it's very handy. and if you want the cut to be precise in the middle, you press ctrl+r, click to get purple line and than 0 and enter. 0 = zero offset.
and you can select a whole line or edge of vertex's by clicking right mouse button and holding alt. doing it twice will get the other "row". just try it.
one time pressing b is rectangular select, twice b is round select, by scrolling you can increase the select area.
Also about loop cutting with ctrl-r, when you have typed ctr-r and the purple line has appeared, scroll the mouse wheel to increase the number of cuts. So if you want to cut a loop into five loops, click ctrl-r and scroll the mouse wheel until five purple lines are visible- then click enter.