Subpanel Configuration

I'm installing a 100 Amp Sub Panel about 3 feet away from my 200 Amp Main Panel. The SubPanel is a Cutler Hammer BR2020B100V and it comes with a pre-installed 100A breaker screwed in (Please see attached photo).

1) I plan to remove the green ground screw/hook in order to separate the left and right bus bars
2) Then add a 100 Amp BR2100 Breaker into the Main Panel and back feed it into the SubPanel 100A Breaker
3) Install lugs in order to accept new wire connections between the 2 panels. In the subpanel I plan on using the right bus bar for all Neutrals (this will be disconnected from the back of the panel) and the left bus bar for all Grounds (this will be grounded to the back of the subpanel by the half inch metal strip that runs from the left bar and underneath the hot bus bar to the green screw).
4) I plan on using Copper Service Entrance Cable 2-2-2-4 (#2 red/hot, #2black/hot, #2white/neutral, #4 green/ground) to connect the 2 panels.

My questions:
A) The panel never came with a dedicated ground bar so would it be okay to use the left bar in the subpanel for all ground wires if I separate it from the right bar or should I purchase a ground bar and install it at the bottom of the subpanel
B) The main panel currently has a bar on the left which has all the #12 and #14 ground wires fed to it plus the service entrance neutral wire. Then there is a bar on the right which has all the #12 and #14 neutral wires fed to it plus the service entrance ground wire. So it seems the neutrals and grounds are bonded in the main panel. I plan on running my SER neutral from the subpanel right bar to the main panel right bar and I plan on running my SER ground from the subpanel left bar to the main panel left bar. Is this okay or does it matter.
C) For the 2 hot wires that run between the 100A breakers, does it matter if I cross the red and black wires or should I tighten down the red wire in the top section of each breaker and tighten down the black wire in the bottom section of each.
D) If I can find it, I plan to buy Copper SER 2-2-2-4 cable to run between the 2 panels which will be inside a stud wall about 3 feet apart. I plan to drill a hole in middle of the stud and run the wire in its jacket without conduit. Would this be acceptable. Also I was offered to use 2/3 Romex wire instead of SER 2-2-2-4 but I'm not sure if this would be a good substitute.

Thanks for any insights you may be able to provide.