OK, glad your're back to working. The Siyah kernel you flashed is for the GT-I9100, the international version of the Galaxy s2. As I said, you will need a kernel that is compiled specifically for the SGH-I777, so get your kernel from the I777 Android Development Forum.
Next, you can also use a straight zImage file with Mobile Odin. You don't have to have a tar. You can even download a ClockworkMod flashable zip file and use an archiving tool such a Win Zip or 7Zip to open it and extract the zImage from it. Then use that to flash through Mobile Odin.
You currently have the stock 3e Recovery, which does not have a backup facility, nor the ability to flash custom firmware (unless it is signed by Samsung.) So you need to install a custom kernel with ClockworkMod Recovery (or TWRP Recovery will also work.) By the way, those are just different developers versions of almost exactly the same recovery functions, so it doesn't really matter which you use.
For a kernel, go to
this post in the development section and download the third of four which is titled "AJK v2.0.5 NO-SWAP Samsung." As I said above, extract the zImage from the zip and use that to flash in Mobile Odin.
Also on this phone, recovery and the kernel are not separate, they are one unit, so you install the kernel to get the custom recovery. Your steps 2 and 3 are incorrect. Remove step 2 entirely. Step 3 will install both the kernel and the custom recovery. In step 4, you can flash any custom firmware you want. They all come with an included kernel, so it doesn't matter what kernel you start with because after you flash you will have a different kernel anyway.
And finally, don't worry about backing up the stock firmware. If you mess up the flash, or soft brick the phone, you can just reinstall stock as you did before. After you have a custom firmware installed, and have your phone configured exactly the way you want it, then is the time to make a backup, because you can flash to a different custom firmware to try it out, and if you don't like it, you can restore your backup and be back to exactly where you were.