A signature photographed on paper arrives as a white rectangle with writing in it. Dropped onto a document, that white box covers whatever is underneath.
Transparency only survives in formats that support it. Save your finished signature as a PNG. Save it as a JPG and the transparent area comes back as solid white, which puts you exactly where you started.
Contrast makes the cutout clean. Dark ink on white paper separates easily. A ballpoint on cream paper photographed in dim light gives you grey ink on grey paper, and no tool separates those neatly.
Keep the file. A signature you have cut out once can be reused on every document you ever need to sign, which is the whole point of doing it carefully the first time.
Because it was saved as a JPG, or never had its background removed. Both are fixed by cutting out the background and saving as PNG.
That depends on the document and where you are. Many agreements accept one, some require a witnessed or certified signature. Check what your document requires.
No, and this is a good example of why that matters. An image of your signature is worth protecting.