JPG to PNG
Your images never leave this device
Converting a JPG to PNG makes a file that some tools and upload forms insist on. It does not make the image better and it does not give it a transparent background: it stores exactly the pixels the JPG had, losslessly, in a much larger file.
How to convert JPG to PNG
It is worth being blunt about what this cannot do, because it is the most common misunderstanding. The JPG compression artefacts. The faint blocky halos around edges; are pixels now, indistinguishable from real detail, and PNG will preserve them perfectly. Nor does the conversion create transparency: the background is opaque, exactly as it was. Removing a background is a separate editing job, not a format change.
Questions
No. That is an editing operation, not a conversion. The PNG will have the same opaque background the JPG had.
No. It preserves what is there, artefacts included. Nothing can recover detail JPG already discarded.
PNG is lossless and stores every pixel. For a photograph that is typically five to ten times the JPG.
When a system refuses anything but PNG. Some print services, icon pipelines and upload forms do.
No. Everything runs in this page.