So for now, I'm practicing sword and shield skip to no avail, but I want to practice the rest of the run too. Is it a problem to start out with no BiT Save and just doing intro mostly normally, other than not getting early iron boots?

For practice, yeah go ahead. Route will change quite a bit without BiT tho, so see the No S+Q route for the changes.

Are there any other big differences other than having to complete Eldin Twilight all at once to get iron boots instead of warping back to Faron to do Forest Temple partway through? (Looking at BiTE route)

If you do BiT, you have to do S&S Skip, I don't believe the sword is in Rusl's house at all. If you have problems with it, what I found that helped me finally get it is to follow the setups every tutorial says with the black line on the ground, but the angle you need is way bigger than it seems in those videos.

The sword doesn't spawn until the shield does (specifically, the midna text after the shield), and you can't get the shield since the CS with the mayor and the other guy never plays (so you never get to jump to the roofs and can't get in). I ¤believe¤ this is because the area is in the wrong state but I don't know for sure.

So yes, if you do BiT, Sword and Shield Skip is ¤mandatory¤ to beat the game.