What are your intentions? From your first post, you apparently have the windows 7 installation CD to repair the windows bootloader, correct? If that's the case you should be set. If it was a new OEM computer and you installed a non-windows bootloader to the mbr and had to send it in for repairs under warranty, they would probably refuse to help. If there is no warranty, I would suggested installing the Arch Grub2 to the master boot record.
If you look at the bootinfoscript output, the first line indicates windows code in the master boot record. If you go down to the grub.cfg file for Arch (which would show the menu you see on screen when booting) you see the entry is: set root='hd0,msdos7'; that is the correct entry as your Arch boot files are on sda7. If you install Grub2 to the mbr, you should be set with windows also becasue the grub.cfg file menuentry for windows point to sda1 where the windows boot files are.
Since you already have windows in the mbr, you should be able to configure an EasyBCD entry for Arch on sda7. I've only used it once so can't help with that. The link below explains installing Grub to from the (Arch) Live CD. It is on the Ubuntu forums but the process is the same. I don't think Arch uses sudo so just open a terminal and login as root by typing (su -). There should not be a password needed on the Live CD. You might go to the Arch forums to see if they have a more detailed process specific to Arch. Read the link below carefully before proceeding:
https://help.ubuntu.com/community/Gr...rom_the_LiveCD