Does converting to PNG improve image quality?
No. It preserves whatever quality the JPG already has and prevents further loss from future saves, but it cannot recover detail that JPG compression already discarded. Quality improvement has to come from a better source file.
Does the converted PNG have a transparent background?
Not by itself. JPG has no transparency to carry over, so the PNG starts fully opaque. To actually get a transparent background you need to remove it — that is a separate editing step, not something the format conversion does.
Why is the PNG so much larger than the JPG?
Because PNG is lossless. JPG reached its small size by throwing detail away; PNG stores every remaining pixel exactly, so the file grows. For photographic images a several-fold increase is normal.
Are my images uploaded anywhere?
No. The conversion runs entirely in your browser, so the files never leave your device and there is no upload to wait for.