1. MJ2 is the bootloader in the leaked version of AT&Ts 4.3 ROM. MJB is the bootloader from the official release. As far as differences go, the MJ2 will allow you to downgrade to earlier bootloaders, whereas the MJB will brick your phone if you try to downgrade bootloaders to a previous version. I have seen several threads where people stated that they could use the MJB bootloader with older ROMs, just make sure the ROM in question does not try to install a bootloader. The other big difference is that the MJB bootloader will install Knox onto your system, at least I believe Knox is installed by the bootloader and not the ROM.
If you wish to sim unlock your phone without buying a code you would need to do it before installing the MJB bootloader. What I've read about the free unlock says that it must be done from stock 4.1.1, bootloader and all.
2a. The link to the bootloader was a dead end for me also. The link to the modem was viable.
2b. The links within the S3Rx thread lead to zips with bootloader and modem included, as opposed to your first link that had the bootloader and modem separate. The androidhostfile link you posted would have the MJB modem and
bootloader, the other hidden link in the S3Rx thread was for the MJ2 bootloader and MJB modem. Loserskater, the OP of that thread and dev of the S3Rx ROM has stated that he uses the MJB bootloader and modem.
3. You could confirm from terminal emulator if you have root:
or with some of the free Root Checker apps. You would need one that includes build info.
TW 4.1.2, stock, rooted,
Samsung Captivate SGH-i897
Currently CyanogenMod 10.1.3
resurrected from softbrick using 4-2ndtwin's Heimdall OneClick to stock Gingerbread - 2.3.5 - kk4
ROM history Eclair > Froyo > Gingerbread > CM9