Why did my JPG come out bigger than the PNG?
Because the picture is mostly flat colour, such as a chart, a diagram or a simple icon, which PNG stores compactly and JPG does not: a test chart grew by a fifth. Photos shrink as JPG; flat pictures are often better left as PNG.
Why do some converters give a black background?
A transparent pixel still stores a colour underneath, often black, and a converter that simply drops the transparency shows it. Here each PNG is drawn over the colour under Behind a JPG first, so the see-through parts take that colour.
Can I turn the JPG back into a PNG?
Yes, pick PNG under Save as, but neither the detail JPG compression removed nor the transparency comes back: the filled background stays. Keep the original PNG if you may need it again.
How many PNGs can I convert at once?
As many as you drop. They are converted one after another, each up to 50 MB, and several download together as a zip.