I actually also was reluctant to stop doing transparency with them for the same reasons, but I switched to the white background because of coloring technique/transparency reasons (I didn't want to put a thick black border around everything ^^;) and also because a few people were doing things like putting the image on a background that was chosen to compliment the first Serian on the page, so for this example (completely made up) we'll just say it was a bright pink Serian, and the background would be dark purple to make it pop. But then if the second Serian they Bonded was also put on the page and it was, say, almost entirely black, then it just looked really really bad with the thick black line almost unseeable on the dark purple bkg

So the white bkg is kind of the lesser of all evils in that regard as well ^^
As for the "don't mess with the image" rule, it pretty much means "pretend you're just linking the image straight from my website, with no editing at all". So other than that, it's up to you what border you put around it, it can definitely be personalized to your heart's desire ^^ The heart border for Shiro is fine
I'm not sure what editor you're using, but you should be able to add a frame by putting the image in a square with padding that is the thickness of the border and then making the frame the background of the square so that it seems like the frame is part of the image when it isn't

If you need help, I am more than happy to test out the editor by making my own account and seeing if it can be done also ^^
The reason for that rule is so that the quality of the Serians, especially the latter ones, doesn't accidentally get downgraded if the user adds a border to the image itself. Going to get technical here, but there are a bunch of formats (.png, .gif, .jpg, .tif, .svg, .eps, etc) and some of them are lossy and some of them are lossless, but even if you save in a lossless file type like png, an image editor can sometimes (and frequently does) change the original in small ways which can make them look like they're a little bit blurrier, more pixelated, a slightly different color, or other things. It's the sort of thing that would be tough to constantly look for, since the changes can be small enough that a quick glance might show me what I expect to see rather than what actually is.